Deformation of tilting-type derived equivalences for crepant resolutions

TL;DR

This paper investigates how tilting-type derived equivalences between algebraic varieties behave under deformations, with applications to stratified Mukai and Atiyah flops, using tilting bundles.

Contribution

It introduces a method to analyze the deformation behavior of tilting-type equivalences and applies it to specific flop cases in algebraic geometry.

Findings

Tilting-type equivalences can be studied under deformations.

Derived equivalences for stratified Mukai and Atiyah flops are characterized via tilting bundles.

Abstract

We say that an exact equivalence between the derived categories of two algebraic varieties is tilting-type if it is constructed by using tilting bundles. The aim of this article is to understand the behavior of tilting-type equivalences for crepant resolutions under deformations. As an application of the method that we establish in this article, we study the derived equivalence for stratified Mukai flops and stratified Atiyah flops in terms of tilting bundles.