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Journal articles on the topic 'Torus fibrations'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Nicaise, Johannes, Chenyang Xu, and Tony Yue Yu. "The non-archimedean SYZ fibration." Compositio Mathematica 155, no. 5 (2019): 953–72. http://dx.doi.org/10.1112/s0010437x19007152.

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We construct non-archimedean SYZ (Strominger–Yau–Zaslow) fibrations for maximally degenerate Calabi–Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

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2

ANDREAS, B., D. HERNÁNDEZ RUIPÉREZ, and D. SÁNCHEZ GÓMEZ. "STABLE SHEAVES OVER K3 FIBRATIONS." International Journal of Mathematics 21, no. 01 (2010): 25–46. http://dx.doi.org/10.1142/s0129167x10005908.

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We construct stable sheaves over K3 fibrations using a relative Fourier-Mukai transform which describes the sheaves in terms of spectral data similar to the construction for elliptic fibrations. On K3 fibered Calabi–Yau threefolds we show that the Fourier-Mukai transform induces an embedding of the relative Jacobian of spectral line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves a generic torus fibration over the moduli space of curves of the given arithmetic genus on the Calabi–Yau manifold.

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3

Muñoz, Vicente. "Torus rational fibrations." Journal of Pure and Applied Algebra 140, no. 3 (1999): 251–59. http://dx.doi.org/10.1016/s0022-4049(98)00004-8.

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4

RUAN, WEI-DONG. "GENERALIZED SPECIAL LAGRANGIAN TORUS FIBRATION FOR CALABI–YAU HYPERSURFACES IN TORIC VARIETIES I." Communications in Contemporary Mathematics 09, no. 02 (2007): 201–16. http://dx.doi.org/10.1142/s021919970700240x.

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In this paper we start the program of constructing generalized special Lagrangian torus fibrations for Calabi–Yau hypersurfaces in toric varieties near the large complex limit, with respect to the restriction of a toric metric on the toric variety to the Calabi–Yau hypersurface. The construction is based on the deformation of the standard toric generalized special Lagrangian torus fibration of the large complex limit X0. In this paper, we will deal with the region near the smooth top dimensional torus fibers of X0 and its mirror dual situation — the region near the 0-dimensional fibers of X0.

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5

Castaño Bernard, Ricardo, and Diego Matessi. "Lagrangian 3-torus fibrations." Journal of Differential Geometry 81, no. 3 (2009): 483–573. http://dx.doi.org/10.4310/jdg/1236604343.

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6

Donagi, Ron, and Tony Pantev. "Torus fibrations, gerbes, and duality." Memoirs of the American Mathematical Society 193, no. 901 (2008): 0. http://dx.doi.org/10.1090/memo/0901.

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7

Dathe, Hamidou, and Philippe Rukimbira. "Fibrations and contact structures." International Journal of Mathematics and Mathematical Sciences 2005, no. 4 (2005): 555–60. http://dx.doi.org/10.1155/ijmms.2005.555.

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8

SALVAI, MARCOS. "AFFINE MAXIMAL TORUS FIBRATIONS OF A COMPACT LIE GROUP." International Journal of Mathematics 13, no. 03 (2002): 217–25. http://dx.doi.org/10.1142/s0129167x02001216.

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By a generalization of the method developed by Gluck and Warner to characterize the oriented great circle fibrations of the three-sphere, we give, for any compact connected semisimple Lie group G, a general procedure to obtain the continuous fibrations of G by Weyl-oriented affine maximal tori, find conditions for smoothness and provide infinite dimensional spaces of concrete examples.

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9

Evans, Jonathan David, and Mirko Mauri. "Constructing local models for Lagrangian torus fibrations." Annales Henri Lebesgue 4 (May 27, 2021): 537–70. http://dx.doi.org/10.5802/ahl.80.

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10

Fujita, Hajime, Mikio Furuta, and Takahiko Yoshida. "Torus Fibrations and Localization of Index II." Communications in Mathematical Physics 326, no. 3 (2014): 585–633. http://dx.doi.org/10.1007/s00220-014-1890-7.

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11

Fujita, Hajime, Mikio Furuta, and Takahiko Yoshida. "Torus Fibrations and Localization of Index III." Communications in Mathematical Physics 327, no. 3 (2014): 665–89. http://dx.doi.org/10.1007/s00220-014-2039-4.

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12

Ikeda, Toru. "Essential Surfaces in Graph Link Exteriors." Canadian Mathematical Bulletin 52, no. 2 (2009): 257–66. http://dx.doi.org/10.4153/cmb-2009-028-9.

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AbstractAn irreducible graph manifold M contains an essential torus if it is not a special Seifert manifold. WhetherM contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits M into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors.

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13

Galkin, V. A. "ON THE STRUCTURE OF HELICAL AXISYMMETRIC SOLUTIONS OF THE NAVIER-STOKES SYSTEM FOR INCOMPRESSIBLE FLUIDS." Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki 64, no. 5 (2024): 780–90. http://dx.doi.org/10.31857/s0044466924050076.

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A class of exact solutions to the Navier-Stokes equations for axisymmetric vortex flows of incompressible fluids is obtained. Invariant manifolds of flows with rotational symmetry relative to a given axis in three-dimensional coordinate space are identified, and the structure of the solutions is described. It is established that typical invariant regions of such flows are rotational figures homeomorphic to a torus, forming a structure of topological fibration, such as in a sphere, cylinder, and more complex configurations composed of such figures. The results are extended to similar solutions

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14

Zharkov, Ilia. "Torus fibrations of Calabi-Yau hypersurfaces in toric varieties." Duke Mathematical Journal 101, no. 2 (2000): 237–57. http://dx.doi.org/10.1215/s0012-7094-00-10124-x.

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15

CASTELLANA, NATÀLIA, and NITU KITCHLOO. "A homotopy construction of the adjoint representation for Lie groups." Mathematical Proceedings of the Cambridge Philosophical Society 133, no. 3 (2002): 399–409. http://dx.doi.org/10.1017/s0305004102005947.

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Let G be a compact, simply-connected, simple Lie group and T ⊂ G a maximal torus. The purpose of this paper is to study the connection between various fibrations over BG (where G is a compact, simply-connected, simple Lie group) associated to the adjoint representation and homotopy colimits over poset categories [Cscr ], hocolim[Cscr ]BGI where GI are certain connected maximal rank subgroups of G.

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16

Chan, Kwokwai, Daniel Pomerleano, and Kazushi Ueda. "Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold." Communications in Mathematical Physics 341, no. 1 (2015): 135–78. http://dx.doi.org/10.1007/s00220-015-2477-7.

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17

Chan, Kwokwai, and Kazushi Ueda. "Dual torus fibrations and homological mirror symmetry for $A_n$-singularities." Communications in Number Theory and Physics 7, no. 2 (2013): 361–96. http://dx.doi.org/10.4310/cntp.2013.v7.n2.a5.

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18

Bode, B., M. R. Dennis, D. Foster, and R. P. King. "Knotted fields and explicit fibrations for lemniscate knots." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2202 (2017): 20160829. http://dx.doi.org/10.1098/rspa.2016.0829.

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We give an explicit construction of complex maps whose nodal lines have the form of lemniscate knots. We review the properties of lemniscate knots, defined as closures of braids where all strands follow the same transverse (1, ℓ) Lissajous figure, and are therefore a subfamily of spiral knots generalizing the torus knots. We then prove that such maps exist and are in fact fibrations with appropriate choices of parameters. We describe how this may be useful in physics for creating knotted fields, in quantum mechanics, optics and generalizing to rational maps with application to the Skyrme–Fadde

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19

NOHARA, YUICHI. "PROJECTIVE EMBEDDINGS AND LAGRANGIAN FIBRATIONS OF KUMMER VARIETIES." International Journal of Mathematics 20, no. 05 (2009): 557–72. http://dx.doi.org/10.1142/s0129167x09005418.

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It is known that holomorphic sections of an ample line bundle L (and its tensor power Lk) over an Abelian variety A are given by theta functions. Moreover, a natural basis of the space of holomorphic sections of L or Lk is related to a certain Lagrangian fibration of A. In our previous paper, we studied projective embeddings of A defined by these basis for Lk. For a natural torus action on the ambient projective space, it is proved that its moment map, restricted to A, approximates the Lagrangian fibration of A for large k, with respect to the "Gromov–Hausdorff topology". In this paper, we pro

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20

Chan, Kwokwai, Naichung Conan Leung, and Changzheng Li. "Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties." Journal of Geometry and Physics 146 (December 2019): 103489. http://dx.doi.org/10.1016/j.geomphys.2019.103489.

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21

MATSUMOTO, Yukio. "Torus fibrations over the $2$ -sphere with the simplest singular fibers." Journal of the Mathematical Society of Japan 37, no. 4 (1985): 605–36. http://dx.doi.org/10.2969/jmsj/03740605.

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22

Fino, Anna, Gueo Grantcharov, and Luigi Vezzoni. "Astheno–Kähler and Balanced Structures on Fibrations." International Mathematics Research Notices 2019, no. 22 (2017): 7093–117. http://dx.doi.org/10.1093/imrn/rnx337.

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Abstract We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, strong Kähler with torsion (SKT), and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then we provide a construction of astheno-Kähler structures on torus bundles over Kähler manifolds leading to new examples. In particular, we find examples of compact complex non-Kähler manifolds which admit a balanced and an astheno-Kähler metric

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23

SMEETS, ARNE. "Principes locaux-globaux pour certaines fibrations en torseurs sous un tore." Mathematical Proceedings of the Cambridge Philosophical Society 158, no. 1 (2014): 131–45. http://dx.doi.org/10.1017/s0305004114000577.

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AbstractLetkbe a number field andTak-torus. Consider a family of torsors underT, i.e. a morphismf:X→ ℙ1kfrom a projective, smoothk-varietyXto ℙ1k, the generic fibreXη→ η of which is a smooth compactification of a principal homogeneous space underT⊗kη. We study the Brauer–Manin obstruction to the Hasse principle and to weak approximation forX, assuming Schinzel's hypothesis. We generalise Wei's recent results [21]. Our results are unconditional ifk=Qand all non-split fibres offare defined overQ. We also establish an unconditional analogue of our main result for zero-cycles of degree 1.

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24

Morrison, David R., and M. Ronen Plesser. "Special Lagrangian torus fibrations of complete intersection Calabi–Yau manifolds: A geometric conjecture." Nuclear Physics B 898 (September 2015): 751–70. http://dx.doi.org/10.1016/j.nuclphysb.2015.05.030.

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25

Stipsicz, András I., and Ki-Heon Yun. "On the minimal number of singular fibers in Lefschetz fibrations over the torus." Proceedings of the American Mathematical Society 145, no. 8 (2017): 3607–16. http://dx.doi.org/10.1090/proc/13480.

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26

Schulz, M. B. "Superstring orientifolds with torsion: O5 orientifolds of torus fibrations and their massless spectra." Fortschritte der Physik 52, no. 10 (2004): 963–1040. http://dx.doi.org/10.1002/prop.200410172.

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27

Groman, Yoel, and Umut Varolgunes. "Locality of relative symplectic cohomology for complete embeddings." Compositio Mathematica 159, no. 12 (2023): 2551–637. http://dx.doi.org/10.1112/s0010437x23007492.

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A complete embedding is a symplectic embedding $\iota :Y\to M$ of a geometrically bounded symplectic manifold $Y$ into another geometrically bounded symplectic manifold $M$ of the same dimension. When $Y$ satisfies an additional finiteness hypothesis, we prove that the truncated relative symplectic cohomology of a compact subset $K$ inside $Y$ is naturally isomorphic to that of its image $\iota (K)$ inside $M$ . Under the assumption that the torsion exponents of $K$ are bounded, we deduce the same result for relative symplectic cohomology. We introduce a technique for constructing complete emb

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28

Clark, Alex, and Lorenzo Sadun. "Small Cocycles, Fine Torus Fibrations, and a $$\varvec{\mathbb {Z}^{2}}$$ Z 2 Subshift with Neither." Annales Henri Poincaré 18, no. 7 (2017): 2301–26. http://dx.doi.org/10.1007/s00023-017-0579-9.

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29

CHEN, JINGYI. "SPECIAL LAGRANGIAN CYCLES AND HERMITIAN YANG–MILLS CONNECTIONS." Communications in Contemporary Mathematics 06, no. 01 (2004): 25–59. http://dx.doi.org/10.1142/s0219199704001227.

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We consider the adiabatic limit of a sequence of Hermitian Yang–Mills connections on a SU(r)-bundle over a semi-flat smooth special Lagrangian torus fibration π:M→B. The restriction of these connections to the fiber tori can be viewed as a family of SU(r)-connections on the fiber tori which are parameterized by B. We show that there is a gauge equivalent subsequence such that the restriction of each connection to the fiber tori converges in the Hausdorff topology, away from some closed subset of B of codimension at least two, to a limit which defines a r-sheeted special Lagrangian cycle in the

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30

Turiel, Francisco-Javier. "Fibrations 2-isotropes en tores." Comptes Rendus Mathematique 347, no. 1-2 (2009): 77–80. http://dx.doi.org/10.1016/j.crma.2008.11.012.

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31

Fang, Fuquan, and Yuguang Zhang. "G 2-manifolds and coassociative torus fibration." Frontiers of Mathematics in China 3, no. 1 (2008): 49–77. http://dx.doi.org/10.1007/s11464-008-0004-2.

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32

Turiel, Francisco-Javier. "Fibrations en tores et -formes de Liouville en dimension." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 333, no. 11 (2001): 995–98. http://dx.doi.org/10.1016/s0764-4442(01)02170-x.

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33

Bonatti, Christian. "Diffeomorphismes commutants des surfaces et stabilite des fibrations en tores." Topology 29, no. 1 (1990): 101–26. http://dx.doi.org/10.1016/0040-9383(90)90027-h.

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34

Bennai, M., and E. H. Saidi. "NC Calabi–Yau manifolds in toric varieties with NC torus fibration." Physics Letters B 550, no. 1-2 (2002): 108–16. http://dx.doi.org/10.1016/s0370-2693(02)02962-3.

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35

Fitzpatrick, Sean. "On the Geometry of Almost -Manifolds." ISRN Geometry 2011 (December 13, 2011): 1–12. http://dx.doi.org/10.5402/2011/879042.

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An -structure on a manifold is an endomorphism field satisfying . We call an f-structure regular if the distribution is involutive and regular, in the sense of Palais. We show that when a regular f-structure on a compact manifold M is an almost -structure, it determines a torus fibration of M over a symplectic manifold. When rank , this result reduces to the Boothby-Wang theorem. Unlike similar results for manifolds with -structure or -structure, we do not assume that the f-structure is normal. We also show that given an almost -structure, we obtain an associated Jacobi structure, as well as a

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36

Heil, Wolfgang, and Wilbur Whitten. "The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds." Canadian Mathematical Bulletin 37, no. 4 (1994): 482–89. http://dx.doi.org/10.4153/cmb-1994-070-7.

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AbstractThe Seifert-fiber-space conjecture for nonorientable 3-manifolds states that if M denotes a compact, irreducible, nonorientable 3-manifold that is not a fake P2 x S1, if π1M is infinite and does not contain Z2 * Z2 as a subgroup, and if π1M does however contain a nontrivial, cyclic, normal subgroup, then M is a Seifert bundle. In this paper, we construct all compact, irreducible, nonorientable 3-manifolds (that do not contain a fake P2 × I) each of whose fundamental group contains Z2 * Z2 and an infinité cyclic, normal subgroup; none of these manifolds admits a Seifert fibration, but t

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37

Prince, Thomas. "Smoothing Calabi–Yau toric hypersurfaces using the Gross–Siebert algorithm." Compositio Mathematica 157, no. 7 (2021): 1441–91. http://dx.doi.org/10.1112/s0010437x21007132.

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We explain how to form a novel dataset of Calabi–Yau threefolds via the Gross–Siebert algorithm. We expect these to degenerate to Calabi–Yau toric hypersurfaces with certain Gorenstein (not necessarily isolated) singularities. In particular, we explain how to ‘smooth the boundary’ of a class of four-dimensional reflexive polytopes to obtain polarised tropical manifolds. We compute topological invariants of a compactified torus fibration over each such tropical manifold, expected to be homeomorphic to the general fibre of the Gross–Siebert smoothing. We consider a family of examples related to

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38

Dellatorre, Matthew. "The Degenerate Special Lagrangian Equation on Riemannian Manifolds." International Mathematics Research Notices 2020, no. 9 (2018): 2832–63. http://dx.doi.org/10.1093/imrn/rny099.

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Abstract We show that the degenerate special Lagrangian equation (DSL), recently introduced by Rubinstein–Solomon, induces a global equation on every Riemannian manifold, and that for certain associated geometries this equation governs, as it does in the Euclidean setting, geodesics in the space of positive Lagrangians. For example, geodesics in the space of positive Lagrangian sections of a smooth Calabi–Yau torus fibration are governed by the Riemannian DSL on the base manifold. We then develop their analytic techniques, specifically modifications of the Dirichlet duality theory of Harvey–La

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39

BIRMAN, JOAN S., and WILLIAM W. MENASCO. "ON MARKOV'S THEOREM." Journal of Knot Theory and Its Ramifications 11, no. 03 (2002): 295–310. http://dx.doi.org/10.1142/s0218216502001627.

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Let χ be an oriented link type in the oriented 3-sphere S3 or ℝ3 = S3 - {∞}. A representative X ∈ χ is said to be a closed braid if there is an unknotted curve A ⊂ S3 - X (the axis) and a choice of fibration ℋ of the open solid torus S3 - A by meridian discs {Hθ : θ ∈ [0, 2 π]}, such that whenever X meets a fiber Hθ the intersection is transverse. Closed braid representations of χ are not unique, and Markov's well-known theorem asserts that any two are related by a finite sequence of elementary moves. The main result in this paper is to give a new proof of Markov's theorem. We hope that our ne

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40

Zafiris, Elias, and Albrecht von Müller. "Electron Beams on the Brillouin Zone: A Cohomological Approach via Sheaves of Fourier Algebras." Universe 9, no. 9 (2023): 392. http://dx.doi.org/10.3390/universe9090392.

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Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons.

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41

Abouzaid, Mohammed. "Homological mirror symmetry without correction." Journal of the American Mathematical Society 34, no. 4 (2021): 1059–173. http://dx.doi.org/10.1090/jams/973.

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Let X X be a closed symplectic manifold equipped with a Lagrangian torus fibration over a base Q Q . A construction first considered by Kontsevich and Soibelman produces from this data a rigid analytic space Y Y , which can be considered as a variant of the T T -dual introduced by Strominger, Yau, and Zaslow. We prove that the Fukaya category of tautologically unobstructed graded Lagrangians in X X embeds fully faithfully in the derived category of (twisted) coherent sheaves on Y Y , under the technical assumption that π 2 ( Q ) \pi _2(Q) vanishes (all known examples satisfy this assumption).

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42

Ruan, W. D. "Lagrangian torus fibration of quintic Calabi-Yau hypersufaces II: Technical results on gradient flow construction." Journal of Symplectic Geometry 1, no. 3 (2001): 435–522. http://dx.doi.org/10.4310/jsg.2001.v1.n3.a1.

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43

Hamada, Noriyuki. "Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus." Michigan Mathematical Journal 63, no. 2 (2014): 275–91. http://dx.doi.org/10.1307/mmj/1401973051.

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44

Ruan, Wei-Dong. "Lagrangian Torus Fibration of Quintic Calabi-Yau Hypersurfaces III: Symplectic Topological Syz Mirror Construction for General Quintics." Journal of Differential Geometry 63, no. 2 (2003): 171–229. http://dx.doi.org/10.4310/jdg/1090426677.

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45

Shelukhin, Egor, Dmitry Tonkonog, and Renato Vianna. "Geometry of symplectic flux and Lagrangian torus fibrations." Journal of Topology 17, no. 4 (2024). http://dx.doi.org/10.1112/topo.70002.

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AbstractSymplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define using its Fukaya algebra. The main geometric feature of the invariant is its concavity over isotopies with linear flux. We derive constraints on flux, Weinstein neighbourhood embeddings and holomorphic disk potentials for Gelfand–Cetlin fibres of Fano varieties in terms of their polytopes. We also describe the space of fibres of almost toric fibrations on the complex projective plane up to Hamiltonian isotopy, a

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46

Nakanishi, Hayato. "Homological mirror symmetry of toric Fano surfaces via Morse homotopy." Journal of Mathematical Physics 65, no. 5 (2024). http://dx.doi.org/10.1063/5.0168792.

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Strominger–Yau–Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus fibrations. We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss the homological mirror symmetry, where we consider Morse homotopy of the moment polytope instead of the Fukaya category.

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47

Schwald, Martin. "On the Definition of Irreducible Holomorphic Symplectic Manifolds and Their Singular Analogs." International Mathematics Research Notices, April 19, 2021. http://dx.doi.org/10.1093/imrn/rnab032.

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Abstract In the definition of irreducible holomorphic symplectic manifolds the condition of being simply connected can be replaced by vanishing irregularity. We discuss holomorphic symplectic, finite quotients of complex tori with ${\operatorname{h}}^0(X,\,\Omega ^{[2]}_X)=1$ and their Lagrangian fibrations. Neither $X$ nor the base can be smooth unless $X$ is a $2$-torus.

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48

Sheridan, Nick, and Ivan Smith. "Lagrangian cobordism and tropical curves." Journal für die reine und angewandte Mathematik (Crelles Journal), November 7, 2020. http://dx.doi.org/10.1515/crelle-2020-0035.

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AbstractWe study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism group is a divisible group. The results are independent of but motivated by mirror symmetry, and

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49

"Singular Lagrangian torus fibrations on the smoothing of algebraic cones." Journal of Symplectic Geometry 22, no. 4 (2024): 847–913. http://dx.doi.org/10.4310/jsg.241021223611.

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50

Stipsicz, András I., and Ki-Heon Yun. "Minimal number of singular fibers in Lefschetz fibrations over the torus." Proceedings of the American Mathematical Society, May 6, 2016, 1. http://dx.doi.org/10.1090/proc/13267.

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