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Journal articles on the topic 'Irreducible holomorphic symplectic manifolds'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Camere, Chiara. "Lattice polarized irreducible holomorphic symplectic manifolds." Annales de l’institut Fourier 66, no. 2 (2016): 687–709. http://dx.doi.org/10.5802/aif.3022.

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2

Boissière, Samuel, Marc Nieper-Wißkirchen, and Alessandra Sarti. "Smith theory and irreducible holomorphic symplectic manifolds." Journal of Topology 6, no. 2 (2013): 361–90. http://dx.doi.org/10.1112/jtopol/jtt002.

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3

Franco, Emilio, Marcos Jardim, and Grégoire Menet. "Brane involutions on irreducible holomorphic symplectic manifolds." Kyoto Journal of Mathematics 59, no. 1 (2019): 195–235. http://dx.doi.org/10.1215/21562261-2018-0009.

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4

Camere, Chiara. "Some remarks on moduli spaces of lattice polarized holomorphic symplectic manifolds." Communications in Contemporary Mathematics 20, no. 04 (2018): 1750044. http://dx.doi.org/10.1142/s0219199717500444.

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We construct quasi-projective moduli spaces of [Formula: see text]-general lattice polarized irreducible holomorphic symplectic manifolds. Moreover, we study their Baily–Borel compactification and investigate a relation between one-dimensional boundary components and equivalence classes of rational Lagrangian fibrations defined on mirror manifolds.

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5

Braverman, Maxim. "Symplectic cutting of Kähler manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 508 (1999): 85–98. http://dx.doi.org/10.1515/crll.1999.508.85.

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Abstract We obtain estimates on the character of the cohomology of an S1-equivariant holomorphic vector bundle over a Kähler manifold M in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of M. In particular, we prove and extend inequalities conjectured by Wu and Zhang. The proof is based on constructing a flat family of complex spaces Mt (t ∈ ℂ) such that Mt is isomorphic to M for t ≠ 0, while M0 is a singular reducible complex space, whose irreducible components are the Lerman symplectic cuts.

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6

Amerik, Ekaterina, and Misha Verbitsky. "Construction of automorphisms of hyperkähler manifolds." Compositio Mathematica 153, no. 8 (2017): 1610–21. http://dx.doi.org/10.1112/s0010437x17007138.

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Let $M$ be an irreducible holomorphic symplectic (hyperkähler) manifold. If $b_{2}(M)\geqslant 5$, we construct a deformation $M^{\prime }$ of $M$ which admits a symplectic automorphism of infinite order. This automorphism is hyperbolic, that is, its action on the space of real $(1,1)$-classes is hyperbolic. If $b_{2}(M)\geqslant 14$, similarly, we construct a deformation which admits a parabolic automorphism (and many other automorphisms as well).

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7

Brecan, Ana-Maria, Tim Kirschner, and Martin Schwald. "Unobstructedness of hyperkähler twistor spaces." Mathematische Zeitschrift 300, no. 3 (2021): 2485–517. http://dx.doi.org/10.1007/s00209-021-02841-4.

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AbstractA family of irreducible holomorphic symplectic (ihs) manifolds over the complex projective line has unobstructed deformations if its period map is an embedding. This applies in particular to twistor spaces of ihs manifolds. Moreover, a family of ihs manifolds over a subspace of the period domain extends to a universal family over an open neighborhood in the period domain.

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8

Camere, Chiara, Grzegorz Kapustka, Michał Kapustka, and Giovanni Mongardi. "Verra Four-Folds, Twisted Sheaves, and the Last Involution." International Mathematics Research Notices 2019, no. 21 (2018): 6661–710. http://dx.doi.org/10.1093/imrn/rnx327.

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Abstract We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3[2]-type admitting non-symplectic involutions with invariant lattices U(2) ⊕ D4(−1) or U(2) ⊕ E8(−2). This complements the results obtained in [43], [13], and the results from [29] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using

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9

Golla, Marco, and Laura Starkston. "The symplectic isotopy problem for rational cuspidal curves." Compositio Mathematica 158, no. 7 (2022): 1595–682. http://dx.doi.org/10.1112/s0010437x2200762x.

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We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to five, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic vers

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10

Mongardi, Giovanni, Antonio Rapagnetta, and Giulia Saccà. "The Hodge diamond of O’Grady’s six-dimensional example." Compositio Mathematica 154, no. 5 (2018): 984–1013. http://dx.doi.org/10.1112/s0010437x1700803x.

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We realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of$\text{K3}^{[3]}$type by a birational involution, thereby computing its Hodge numbers.

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11

Knutsen, Andreas Leopold, Margherita Lelli-Chiesa, and Giovanni Mongardi. "Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds." Transactions of the American Mathematical Society 371, no. 2 (2018): 1403–38. http://dx.doi.org/10.1090/tran/7340.

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12

Lo Bianco, Federico. "On the Primitivity of Birational Transformations of Irreducible Holomorphic Symplectic Manifolds." International Mathematics Research Notices 2019, no. 1 (2017): 1–32. http://dx.doi.org/10.1093/imrn/rnx109.

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13

Iliev, Atanas, Grzegorz Kapustka, Michał Kapustka, and Kristian Ranestad. "EPW cubes." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 748 (2019): 241–68. http://dx.doi.org/10.1515/crelle-2016-0044.

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Abstract We construct a new 20-dimensional family of projective six-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 surface and are constructed as natural double covers of special codimension-three subvarieties of the Grassmannian G(3,6) . These codimension-three subvarieties are defined as Lagrangian degeneracy loci and their construction is parallel to that of EPW sextics, we call them the EPW cubes. As a consequence we prove that the moduli space of polarized IHS sixfolds of K3 -

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14

Ouchi, Genki. "Lagrangian embeddings of cubic fourfolds containing a plane." Compositio Mathematica 153, no. 5 (2017): 947–72. http://dx.doi.org/10.1112/s0010437x16008307.

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We prove that a very general smooth cubic fourfold containing a plane can be embedded into an irreducible holomorphic symplectic eightfold as a Lagrangian submanifold. We construct the desired irreducible holomorphic symplectic eightfold as a moduli space of Bridgeland stable objects in the derived category of the twisted K3 surface corresponding to the cubic fourfold containing a plane.

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15

Zehmisch, Kai. "Holomorphic jets in symplectic manifolds." Journal of Fixed Point Theory and Applications 17, no. 2 (2014): 379–402. http://dx.doi.org/10.1007/s11784-014-0178-z.

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16

Mongardi, Giovanni, and John Christian Ottem. "Curve classes on irreducible holomorphic symplectic varieties." Communications in Contemporary Mathematics 22, no. 07 (2019): 1950078. http://dx.doi.org/10.1142/s0219199719500780.

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We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of [Formula: see text]-type and of generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.

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17

Beauville, Arnaud. "Antisymplectic involutions of holomorphic symplectic manifolds." Journal of Topology 4, no. 2 (2011): 300–304. http://dx.doi.org/10.1112/jtopol/jtr002.

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18

Gromov, M. "Pseudo holomorphic curves in symplectic manifolds." Inventiones Mathematicae 82, no. 2 (1985): 307–47. http://dx.doi.org/10.1007/bf01388806.

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19

Broka, Damien, and Ping Xu. "Symplectic realizations of holomorphic Poisson manifolds." Mathematical Research Letters 29, no. 4 (2022): 903–44. http://dx.doi.org/10.4310/mrl.2022.v29.n4.a1.

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20

Charles, François, Giovanni Mongardi, and Gianluca Pacienza. "Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles." Compositio Mathematica 160, no. 2 (2023): 288–316. http://dx.doi.org/10.1112/s0010437x20007526.

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We study families of rational curves on irreducible holomorphic symplectic varieties. We give a necessary and sufficient condition for a sufficiently ample linear system on a holomorphic symplectic variety of $K3^{[n]}$ -type to contain a uniruled divisor covered by rational curves of primitive class. In particular, for any fixed $n$ , we show that there are only finitely many polarization types of holomorphic symplectic variety of $K3^{[n]}$ -type that do not contain such a uniruled divisor. As an application, we provide a generalization of a result due to Beauville–Voisin on the Chow group o

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21

Gritsenko, V., K. Hulek, and G. K. Sankaran. "Moduli spaces of irreducible symplectic manifolds." Compositio Mathematica 146, no. 2 (2010): 404–34. http://dx.doi.org/10.1112/s0010437x0900445x.

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AbstractWe study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of polarised deformation K3[2]manifolds with polarisation of degree 2dand split type is of general type ifd≥12.

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22

Mongardi, G., and M. Wandel. "Induced automorphisms on irreducible symplectic manifolds:." Journal of the London Mathematical Society 92, no. 1 (2015): 123–43. http://dx.doi.org/10.1112/jlms/jdv012.

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23

Hwang, Jun-Muk. "Base manifolds for fibrations of projective irreducible symplectic manifolds." Inventiones mathematicae 174, no. 3 (2008): 625–44. http://dx.doi.org/10.1007/s00222-008-0143-9.

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24

Ran, Ziv. "Deformations of holomorphic pseudo-symplectic Poisson manifolds." Advances in Mathematics 304 (January 2017): 1156–75. http://dx.doi.org/10.1016/j.aim.2016.09.016.

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25

Mongardi, Giovanni. "On the monodromy of irreducible symplectic manifolds." Algebraic Geometry 3, no. 3 (2016): 385–91. http://dx.doi.org/10.14231/ag-2016-017.

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26

Polterovich, Leonid. "Symplectic displacement energy for Lagrangian submanifolds." Ergodic Theory and Dynamical Systems 13, no. 2 (1993): 357–67. http://dx.doi.org/10.1017/s0143385700007410.

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AbstractRecently H. Hofer defined a new symplectic invariant which has a beautiful dynamical meaning. In the present paper we study this invariant for Lagrangian submanifolds of symplectic manifolds. Our approach is based on Gromov's theory of pseudo-holomorphic curves.

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27

HIND, R. "STEIN FILLINGS OF LENS SPACES." Communications in Contemporary Mathematics 05, no. 06 (2003): 967–82. http://dx.doi.org/10.1142/s0219199703001178.

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We describe a foliation by finite energy holomorphic curves of some symplectic manifolds which are constructed from Stein manifolds with Lens space boundaries. One application is that all such Stein manifolds bounded by the same contact Lens space are equivalent up to Stein homotopy.

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28

DUISTERMAAT, J. J., and A. PELAYO. "COMPLEX STRUCTURES ON FOUR-MANIFOLDS WITH SYMPLECTIC TWO-TORUS ACTIONS." International Journal of Mathematics 22, no. 03 (2011): 449–63. http://dx.doi.org/10.1142/s0129167x11006854.

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We apply the general theory for symplectic torus actions with symplectic or coisotropic orbits to prove that a four-manifold with a symplectic two-torus action admits an invariant complex structure and give an identification of those that do not admit a Kähler structure with Kodaira's class of complex surfaces which admit a nowhere vanishing holomorphic (2,0)-form, but are not a torus nor a K3 surface.

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29

Hassett, Brendan, and Yuri Tschinkel. "Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces." Journal of the Institute of Mathematics of Jussieu 9, no. 1 (2009): 125–53. http://dx.doi.org/10.1017/s1474748009000140.

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AbstractWe study the birational geometry of irreducible holomorphic symplectic varieties arising as varieties of lines of general cubic fourfolds containing a cubic scroll. We compute the ample and moving cones, and exhibit a birational automorphism of infinite order explaining the chamber decomposition of the moving cone.

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30

Ye, Rugang. "Filling by holomorphic curves in symplectic 4-manifolds." Transactions of the American Mathematical Society 350, no. 1 (1998): 213–50. http://dx.doi.org/10.1090/s0002-9947-98-01970-9.

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31

O’Grady, K. G. "Involutions and linear systems on holomorphic symplectic manifolds." GAFA Geometric And Functional Analysis 15, no. 6 (2005): 1223–74. http://dx.doi.org/10.1007/s00039-005-0538-3.

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32

Matsushita, Daisuke. "Equidimensionality of Lagrangian fibrations on holomorphic symplectic manifolds." Mathematical Research Letters 7, no. 4 (2000): 389–91. http://dx.doi.org/10.4310/mrl.2000.v7.n4.a4.

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33

Lehn, Christian. "Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds." Mathematical Research Letters 23, no. 2 (2016): 473–97. http://dx.doi.org/10.4310/mrl.2016.v23.n2.a9.

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34

Matsushita, Daisuke. "On nef reductions of projective irreducible symplectic manifolds." Mathematische Zeitschrift 258, no. 2 (2007): 267–70. http://dx.doi.org/10.1007/s00209-007-0160-1.

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35

GEIGES, HANSJÖRG, and KAI ZEHMISCH. "Symplectic cobordisms and the strong Weinstein conjecture." Mathematical Proceedings of the Cambridge Philosophical Society 153, no. 2 (2012): 261–79. http://dx.doi.org/10.1017/s0305004112000163.

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AbstractWe study holomorphic spheres in certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this to confirm the strong Weinstein conjecture (predicting the existence of null-homologous Reeb links) for various higher-dimensional contact manifolds, including contact type hypersurfaces in subcritical Stein manifolds and in some cotangent bundles. The quantitative character of this result leads to the definition of a symplectic capacity.

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36

Mongardi, Giovanni, and Claudio Onorati. "Birational geometry of irreducible holomorphic symplectic tenfolds of O’Grady type." Mathematische Zeitschrift 300, no. 4 (2022): 3497–526. http://dx.doi.org/10.1007/s00209-021-02966-6.

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37

KOVALEV, ALEXEI, and NAM-HOON LEE. "K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 151, no. 2 (2011): 193–218. http://dx.doi.org/10.1017/s030500411100003x.

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AbstractWe consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G2 developed by the first named author. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors and the latter K3 surfaces should satisfy a certain ‘matching condition’ intertwining on their periods and Kähler classes. Suitable examples of threefolds were previously obtained by blowing up curves in Fano threefolds.In this paper, we give a large new class of suitable algebraic threefolds using theory of K3 surfaces with non-symplectic involution due

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38

Tardini, Nicoletta, and Adriano Tomassini. "On the cohomology of almost-complex and symplectic manifolds and proper surjective maps." International Journal of Mathematics 27, no. 12 (2016): 1650103. http://dx.doi.org/10.1142/s0129167x16501032.

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Let [Formula: see text] be an almost-complex manifold. In [Comparing tamed and compatible symplectic cones and cohomological properties of almost-complex manifolds, Comm. Anal. Geom. 17 (2009) 651–683], Li and Zhang introduce [Formula: see text] as the cohomology subgroups of the [Formula: see text]th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds, we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology

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39

Nieper, Marc A. "Hirzebruch-Riemann-Roch formulae on irreducible symplectic Kähler manifolds." Journal of Algebraic Geometry 12, no. 4 (2003): 715–39. http://dx.doi.org/10.1090/s1056-3911-03-00325-4.

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40

Szabó, Zoltán. "Simply-connected irreducible 4-manifolds with no symplectic structures." Inventiones Mathematicae 132, no. 3 (1998): 457–66. http://dx.doi.org/10.1007/s002220050230.

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41

MARKUSHEVICH, D., and A. S. TIKHOMIROV. "NEW SYMPLECTIC V-MANIFOLDS OF DIMENSION FOUR VIA THE RELATIVE COMPACTIFIED PRYMIAN." International Journal of Mathematics 18, no. 10 (2007): 1187–224. http://dx.doi.org/10.1142/s0129167x07004503.

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Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's flop. They have the same singularities as two of Fujiki's examples, namely, 28 isolated singular points analytically equivalent to the Veronese cone of degree 8, but a different Euler number. The family of curves used in this construction forms a linear system on a K3 surface with involution. The structure morphism of both Prymians to the base of the family is

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42

Fu, Lie, and Grégoire Menet. "On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four." Mathematische Zeitschrift 299, no. 1-2 (2021): 203–31. http://dx.doi.org/10.1007/s00209-020-02682-7.

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AbstractWe extend a result of Guan by showing that the second Betti number of a 4-dimensional primitively symplectic orbifold is at most 23 and there are at most 91 singular points. The maximal possibility 23 can only occur in the smooth case. In addition to the known smooth examples with second Betti numbers 7 and 23, we provide examples of such orbifolds with second Betti numbers 3, 5, 6, 8, 9, 10, 11, 14 and 16. In an appendix, we extend Salamon’s relation among Betti/Hodge numbers of symplectic manifolds to symplectic orbifolds.

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43

DORFMEISTER, JOSEF G., and TIAN-JUN LI. "RELATIVE RUAN AND GROMOV–TAUBES INVARIANTS OF SYMPLECTIC 4-MANIFOLDS." Communications in Contemporary Mathematics 15, no. 01 (2013): 1250062. http://dx.doi.org/10.1142/s0219199712500629.

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We define relative Ruan invariants that count embedded connected symplectic submanifolds which contact a fixed symplectic hypersurface V in a symplectic 4-manifold (X, ω) at prescribed points with prescribed contact orders (in addition to insertions on X\V). We obtain invariants of the deformation class of (X, V, ω). Two large issues must be tackled to define such invariants: (1) curves lying in the hypersurface V and (2) genericity results for almost complex structures constrained to make V pseudo-holomorphic (or almost complex). Moreover, these invariants are refined to take into account rim

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44

Ali, Danish, Johann Davidov, and Oleg Mushkarov. "Holomorphic curvatures of twistor spaces." International Journal of Geometric Methods in Modern Physics 11, no. 03 (2014): 1450022. http://dx.doi.org/10.1142/s0219887814500224.

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We study the twistor spaces of oriented Riemannian 4-manifolds as a source of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In particular, we obtain explicit formulas for these curvatures in the case when the base manifold is Einstein and self-dual, and observe that the "squashed" metric on ℂℙ3 is a non-Kähler Hermitian–Einstein metric of positive holomorphic bisectional curvature. This shows that a recent result of Kalafat and Koca [M. Kalafat and C. Koca, Einstein–Hermitian 4-manifolds of positive bisectional curva

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45

Jabuka, Stanislav. "Symplectic surfaces and generic $J$-holomorphic structures on 4-manifolds." Illinois Journal of Mathematics 48, no. 2 (2004): 675–85. http://dx.doi.org/10.1215/ijm/1258138406.

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46

Szab�, Zolt�n, and Peter Ozsv�th. "Holomorphic triangle invariants and the topology of symplectic four-manifolds." Duke Mathematical Journal 121, no. 1 (2004): 1–34. http://dx.doi.org/10.1215/s0012-7094-04-12111-6.

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47

Matsushita, Daisuke. "On singular fibres of Lagrangian fibrations over holomorphic symplectic manifolds." Mathematische Annalen 321, no. 4 (2001): 755–73. http://dx.doi.org/10.1007/s002080100251.

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48

Namikawa, Y. "Counter-example to global Torelli problem for irreducible symplectic manifolds." Mathematische Annalen 324, no. 4 (2002): 841–45. http://dx.doi.org/10.1007/s00208-002-0344-2.

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49

Nagai, Yasunari. "On monodromies of a degeneration of irreducible symplectic Kähler manifolds." Mathematische Zeitschrift 258, no. 2 (2007): 407–26. http://dx.doi.org/10.1007/s00209-007-0179-3.

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50

Guan, Daniel. "Examples of Compact Simply Connected Holomorphic Symplectic Manifolds Which Are Not Formal." Axioms 14, no. 3 (2025): 226. https://doi.org/10.3390/axioms14030226.

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In this paper, we prove that the complex four dimensional compact holomorphic symplectic manifold we found earlier is not formal. This gives another strong consequence that it is not a topological Kähler manifold. We also conjecture that this is true for the higher dimensional ones.

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