Wall Crossing and the Fourier-Mukai Transform for Grassmann Flops

TL;DR

This paper proves the crepant transformation conjecture for relative Grassmann flops, showing that the GIT quotients' I-functions are related by analytic continuation and a Fourier-Mukai transform, confirming deep geometric and algebraic connections.

Contribution

It establishes the crepant transformation conjecture for relative Grassmann flops and links the symplectic transformation to a Fourier-Mukai transform in K-theory.

Findings

I-functions are related by analytic continuation and symplectic transformation.

The symplectic transformation is compatible with Iritani's integral structure.

The transformation is induced by a Fourier-Mukai transform in K-theory.

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.