环镜单反和拉格朗日球

arXiv - MATH - Symplectic Geometry Pub Date : 2024-09-12 DOI:arxiv-2409.08261

Vivek Shende

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摘要

众所周知，格罗斯-西伯特型环变性的中心纤维满足同调镜像对称性：它的相干剪切范畴等价于某个精确交折射曼弗雷德的包裹 Fukaya 范畴。我们在此证明，在 Calabi-Yau 的情况下，线束的图像由拉格朗日球表示。

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Toric mirror monodromies and Lagrangian spheres

The central fiber of a Gross-Siebert type toric degeneration is known to satisfy homological mirror symmetry: its category of coherent sheaves is equivalent to the wrapped Fukaya category of a certain exact symplectic manifold. Here we show that, in the Calabi-Yau case, the images of line bundles are represented by Lagrangian spheres.

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arXiv - MATH - Symplectic Geometry

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