Abstract

The coherent-constructible correspondence for toric variety assigns to each $n$-dimensional toric variety $X_{\mathrm{\Sigma }}$ a Lagrangian skeleton ${\Lambda }_{\mathrm{\Sigma }}\subset T^{\ast }{T}^n$, such that the derived category of coherent sheaves $\mathrm{Coh}<!--FUNCTION\; APPLICATION-->(X_{\mathrm{\Sigma }})$ is equivalent to the (wrapped) constructible sheaves $S{h}^w(T^n,{\Lambda }_{\mathrm{\Sigma }})$. 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 the window subcategory in variation of GIT to a window skeleton.

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