Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 008, 33 pages      arXiv:2404.12303      https://doi.org/10.3842/SIGMA.2025.008

Wall Crossing and the Fourier-Mukai Transform for Grassmann Flops

Nathan Priddis a, Mark Shoemaker b and Yaoxiong Wen c
a) Department of Mathematics, 275 TMCB, Brigham Young University, Provo, UT 84602, USA
b) Department of Mathematics, Colorado State University, 1874 Campus Delivery Fort Collins, CO 80523, USA
c) School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, South Korea

Received April 26, 2024, in final form January 27, 2025; Published online February 06, 2025

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.

Key words: Fourier-Mukai; Grassmannian flops; wall-crossing; Gromov-Witten theory; variation of GIT.

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