Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry
Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry
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Gaiotto 的拉格朗日子变体通过导出的辛几何
DOI：
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发表时间：
2017
影响因子：
0.6
通讯作者：
N. Rozenblyum
中科院分区：
文献类型：
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作者：
V. Ginzburg;N. Rozenblyum
设BunG为光滑复投影曲线上g束的模空间。基于对镜像对称边界条件的研究，Gaiotto（2016）将G的任何辛表示与T * BunG的拉格朗日子变种相关联。我们给出了一个简单的解释（推广）盖奥托的构造在派生辛几何。这允许考虑一种更一般的设置，其中辛g表示被任意辛流形取代，这些流形配备了哈密顿g作用和乘群的作用，这些作用以正权重新缩放辛形式。
Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T∗BunG. We give a simple interpretation of (a generalization of) Gaiotto’s construction in terms of derived symplectic geometry. This allows to consider a more general setting where symplectic G-representations are replaced by arbitrary symplectic manifolds equipped with a Hamiltonian G-action and with an action of the multiplicative group that rescales the symplectic form with positive weight.