Preservation of stability under the Fourier-Mukai transform whose kernel is the Poincare line bundle

TL;DR

This paper investigates how the Fourier-Mukai transform with the Poincare line bundle kernel preserves Gieseker stability of sheaves on abelian surfaces, contributing to understanding stability behavior under derived equivalences.

Contribution

It demonstrates the preservation of Gieseker stability for sheaves under a specific Fourier-Mukai transform with the Poincare kernel on abelian surfaces.

Findings

Gieseker stability is preserved under the Fourier-Mukai transform with Poincare kernel.

The result applies to sheaves on any abelian surface.

Provides insights into stability preservation in derived categories.

Abstract

For a Fourier-Mukai transform whose kernel is the Poincare line bundle, we study the preservation of Gieseker stability of sheaves on any abelian surface.