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Symplectic vector space

About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.


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TL;DR: In this article, a collection of vector bundles in the derived categories of coherent sheaves on the Grassmannian of isotropic two-dimensional subspaces in a symplectic vector space of dimension 2n and in an orthogonal vector space for all n was constructed.
Abstract: We construct a full exceptional collection of vector bundles in the derived categories of coherent sheaves on the Grassmannian of isotropic two-dimensional subspaces in a symplectic vector space of dimension 2n and in an orthogonal vector space of dimension 2n + 1 for all n.

109 citations

Journal ArticleDOI
TL;DR: In this article, the relation between these classifications for the various nucleon numbers is studied and is found to be governed by another symplectic group, the transformations of which in general change the nucleon number.

107 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Dirac bracket can be used to bring the singular symplectic two-form into a non-degenerated form, by an iterative implementation of the existing constraints.
Abstract: It is shown that the symplectic two-form, which defines the geometrical structure of a constrained theory in the Faddeev-Jackiw approach, may be brought into a non-degenerated form, by an iterative implementation of the existing constraints. The resulting generalized brackets coincide with those obtained by the Dirac bracket approach, if the constrained system under investigation presents only second-class constraints. For gauge theories, a symmetry breaking term must be supplemented to bring the symplectic form into a non-singular configuration. At present, the singular symplectic two-form provides directly the generators of the time independent gauge transformations.

106 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce a symplectic surgery in six dimensions which collapses Lagrangian three-spheres and replaces them by symplectic two-sphere, which corresponds to an operation on complex 3-folds studied by Clemens, Friedman and Tian.
Abstract: We introduce a symplectic surgery in six dimensions which collapses Lagrangian three-spheres and replaces them by symplectic two-spheres. Under mirror symmetry it corresponds to an operation on complex 3-folds studied by Clemens, Friedman and Tian. We describe several examples which show that there are either many more Calabi-Yau manifolds (e.g., rigid ones) than previously thought or there exist "symplectic Calabi-Yaus" — non-Kahler symplectic 6-folds with c1 = 0. The analogous surgery in four dimensions, with a generalisation to ADE-trees of Lagrangians, implies that the canonical class of a minimal complex surface contains symplectic forms if and only if it has positive square.

105 citations

Journal ArticleDOI
TL;DR: In this paper, the Calabi-Yau equation on symplectic manifolds was studied and Donaldson's conjecture on estimates for this equation in terms of a taming symplectic form was reduced to an integral estimate of a scalar potential function under a positive curvature condition.
Abstract: We study the Calabi-Yau equation on symplectic manifolds We show that Donaldson's conjecture on estimates for this equation in terms of a taming symplectic form can be reduced to an integral estimate of a scalar potential function Under a positive curvature condition, we show that the conjecture holds

104 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202310
202221
202113
20208
201910
201818