Wall crossing of the moduli spaces of perverse coherent sheaves on a blow-up

TL;DR

This paper studies how the moduli spaces of perverse coherent sheaves change when crossing walls in the stability space on a blow-up, providing insights into their wall crossing behavior and twisted stability.

Contribution

It offers a detailed analysis of wall crossing phenomena for perverse coherent sheaves on blow-ups, extending Toda's stability conditions and explaining twisted stability transitions.

Findings

Describes wall crossing behavior of perverse coherent sheaves.

Connects wall crossing with Toda's stability condition.

Explains twisted stability in the context of wall crossing.

Abstract

We give a remark on the wall crossing behavior of perverse coherent sheaves on a blow-up and stability condition constructed by Toda. We also explain the wall crossing of twisted stability in terms of stability condition.