Window shifts, flop equivalences and Grassmannian twists

TL;DR

This paper introduces new autoequivalences on derived categories of vector bundles over Grassmannians, arising from Grassmannian flops, generalizing spherical twists, with algebraic and geometric constructions.

Contribution

It presents a novel class of autoequivalences from Grassmannian flops, extending the concept of spherical twists with explicit algebraic and geometric frameworks.

Findings

New autoequivalences from Grassmannian flops

Equivalence of algebraic and geometric constructions

Explicit methods for computations

Abstract

We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel-Thomas spherical twists, which can be seen as arising from standard flops. We first give a simple algebraic construction, which is well-suited to explicit computations. We then give a geometric construction using spherical functors which we prove is equivalent.