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Wall Crossing and the Fourier-Mukai Transform for Grassmann Flops

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arxiv 2404.12303 v2 pith:ZKQ472MZ submitted 2024-04-18 math.AG

Nathan Priddis , Mark Shoemaker , Yaoxiong Wen This is my paper · ORCID
classification math.AG
keywords transformationflopsfourier-mukaigrassmannsymplectictransformanalyticbase
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abstract

We prove the crepant transformation conjecture for relative Grassmann flops over a smooth base $B$. We show that the $I$-functions of the respective GIT quotients are related by analytic continuation and a symplectic transformation. We verify that the symplectic transformation is compatible with Iritani's integral structure, that is, that it is induced by a Fourier-Mukai transform in $K$-theory.

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  1. Quantum spectrum and Gamma structure for standard flips

    math.AG 2025-02 conditional novelty 7.0 of 10

    For standard flips, the extremal quantum spectrum is shown to be compatible with the Gamma-class decomposition and with the semi-orthogonal decompositions of Orlov and Belmans-Fu-Raedschelders.

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