Stability conditions and birational geometry of projective surfaces

TL;DR

This paper demonstrates that the minimal model program for smooth projective surfaces can be understood through the variation of moduli spaces of Bridgeland stable objects in the derived category, linking birational geometry with stability conditions.

Contribution

It establishes a novel connection between the minimal model program and Bridgeland stability conditions on derived categories of surfaces.

Findings

Minimal model program corresponds to variation of Bridgeland moduli spaces.

Bridgeland stability conditions encode birational transformations.

Provides a new perspective on surface classification via derived categories.

Abstract

We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.