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Relevant bibliographies by topics / Symplectic bundles

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Journal articles

Academic literature on the topic 'Symplectic bundles'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Symplectic bundles"

1

Choe, Insong, and George H. Hitching. "Non-defectivity of Grassmannian bundles over a curve." International Journal of Mathematics 27, no. 07 (2016): 1640002. http://dx.doi.org/10.1142/s0129167x16400024.

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Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on ve

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2

Choe, Insong, and G. H. Hitching. "A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve." International Journal of Mathematics 25, no. 05 (2014): 1450047. http://dx.doi.org/10.1142/s0129167x14500475.

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A symplectic or orthogonal bundle V of rank 2n over a curve has an invariant t(V) which measures the maximal degree of its isotropic subbundles of rank n. This invariant t defines stratifications on moduli spaces of symplectic and orthogonal bundles. We study this stratification by relating it to another one given by secant varieties in certain extension spaces. We give a sharp upper bound on t(V), which generalizes the classical Nagata bound for ruled surfaces and the Hirschowitz bound for vector bundles, and study the structure of the stratifications on the moduli spaces. In particular, we c

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3

Benedetti, Gabriele, and Alexander F. Ritter. "Invariance of symplectic cohomology and twisted cotangent bundles over surfaces." International Journal of Mathematics 31, no. 09 (2020): 2050070. http://dx.doi.org/10.1142/s0129167x20500706.

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We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be nonexact and noncompactly supported, provided one uses the correct local system of coefficients in Floer theory. As a sample application beyond the Liouville setup, we describe in detail the symplectic cohomology for disc bundles in the twisted cotangent bundle of surfaces, and we deduce existence results for periodic magnetic geodesics on surfaces. In particular, we show the existence of geometrically distinct orbits by exploiting properties of the

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4

CHOE, INSONG, and GEORGE H. HITCHING. "Lagrangian subbundles of symplectic bundles over a curve." Mathematical Proceedings of the Cambridge Philosophical Society 153, no. 2 (2012): 193–214. http://dx.doi.org/10.1017/s0305004112000096.

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AbstractA symplectic bundle over an algebraic curve has a natural invariantsLagdetermined by the maximal degree of its Lagrangian subbundles. This can be viewed as a generalization of the classical Segre invariants of a vector bundle. We give a sharp upper bound onsLagwhich is analogous to the Hirschowitz bound on the classical Segre invariants. Furthermore, we study the stratifications induced bysLagon moduli spaces of symplectic bundles, and get a full picture for the case of rank four.

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5

Bakuradze, M. "On the Buchstaber Subring in MSp∗." gmj 5, no. 5 (1998): 401–14. http://dx.doi.org/10.1515/gmj.1998.401.

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Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

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6

HITCHING, GEORGE H. "RANK FOUR SYMPLECTIC BUNDLES WITHOUT THETA DIVISORS OVER A CURVE OF GENUS TWO." International Journal of Mathematics 19, no. 04 (2008): 387–420. http://dx.doi.org/10.1142/s0129167x08004716.

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The moduli space [Formula: see text] of rank four semistable symplectic vector bundles over a curve X of genus two is an irreducible projective variety of dimension ten. Its Picard group is generated by the determinantal line bundle Ξ. The base locus of the linear system |Ξ| consists of precisely those bundles without theta divisors, that is, admitting nonzero maps from every line bundle of degree -1 over X. We show that this base locus consists of six distinct points, which are in canonical bijection with the Weierstrass points of the curve. We relate our construction of these bundles to anot

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7

de Araujo, Artur. "Generalized quivers, orthogonal and symplectic representations, and Hitchin–Kobayashi correspondences." International Journal of Mathematics 30, no. 03 (2019): 1850085. http://dx.doi.org/10.1142/s0129167x18500854.

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We review the theory of quiver bundles over a Kähler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group [Formula: see text]. We first study the case when [Formula: see text] or [Formula: see text], interpreting them as orthogonal (respectively symplectic) bundle representations of the symmetric quivers introduced by Derksen–Weyman. We also study supermixed quivers, which simultaneously involve both orthogonal and symplectic symmetries. In particular, we completely characterize the polystable forms of such representations. Finally, we discuss

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8

BISWAS, INDRANIL, та SARBESWAR PAL. "ON MODULI SPACE OF HIGGS Gp(2n, ℂ)-BUNDLES OVER A RIEMANN SURFACE". International Journal of Geometric Methods in Modern Physics 07, № 02 (2010): 311–22. http://dx.doi.org/10.1142/s0219887810004002.

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Let X be a compact connected Riemann surface; the holomorphic cotangent bundle of X will be denoted by KX. Let [Formula: see text] denote the moduli space of semistable Higgs Gp (2n, ℂ)-bundles over X of fixed topological type. The complex variety [Formula: see text] has a natural holomorphic symplectic structure. On the other hand, for any ℓ ≥ 1, the Liouville symplectic from on the total space of KX defines a holomorphic symplectic structure on the Hilbert scheme Hilb ℓ(KX) parametrizing the zero-dimensional subschemes of KX. We relate the symplectic form on Hilb ℓ(KX) with the symplectic fo

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9

BISWAS, INDRANIL, TOMAS L. GÓMEZ, and VICENTE MUÑOZ. "AUTOMORPHISMS OF MODULI SPACES OF SYMPLECTIC BUNDLES." International Journal of Mathematics 23, no. 05 (2012): 1250052. http://dx.doi.org/10.1142/s0129167x12500528.

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Let X be an irreducible smooth complex projective curve of genus g ≥ 4. Fix a line bundle L on X. Let MSp(L) be the moduli space of semistable symplectic bundles (E, φ : E ⊗ E → L) on X, with the symplectic form taking values in L. We show that the automorphism group of MSp(L) is generated by the automorphisms of the form E ↦ E ⊗ M, where [Formula: see text], together with the automorphisms induced by automorphisms of X.

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10

Otiman, Alexandra. "Locally conformally symplectic bundles." Journal of Symplectic Geometry 16, no. 5 (2018): 1377–408. http://dx.doi.org/10.4310/jsg.2018.v16.n5.a5.

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