Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916648594702336 |
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| author | Zhou, Peng |
| author_facet | Zhou, Peng |
| contents | Coherent-Constructible Correspondence for toric variety assigns to each $n$-dimensional toric variety $X_Σ$ a Lagrangian skeleton $Λ_Σ\subset T^*T^n$, such that the derived category of coherent sheaves $Coh(X_Σ)$ is equivalent to the (wrapped) constructible sheaves $Sh^w(T^n, Λ_Σ)$. In this paper, we extend this correspondence, so that flip and flop between toric varieties corresponds to variation of Lagrangian skeletons. The main idea is to translate window subcategory in variation of GIT to a window skeleton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_03719 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop Zhou, Peng Symplectic Geometry 57R17 Coherent-Constructible Correspondence for toric variety assigns to each $n$-dimensional toric variety $X_Σ$ a Lagrangian skeleton $Λ_Σ\subset T^*T^n$, such that the derived category of coherent sheaves $Coh(X_Σ)$ is equivalent to the (wrapped) constructible sheaves $Sh^w(T^n, Λ_Σ)$. In this paper, we extend this correspondence, so that flip and flop between toric varieties corresponds to variation of Lagrangian skeletons. The main idea is to translate window subcategory in variation of GIT to a window skeleton. |
| title | Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop |
| topic | Symplectic Geometry 57R17 |
| url | https://arxiv.org/abs/2011.03719 |