The noncommutative MMP for blowup surfaces

TL;DR

This paper develops a noncommutative minimal model program for surface blowups, constructing quasi-convergent paths in Bridgeland stability space that yield various semiorthogonal decompositions, advancing understanding of derived categories in algebraic geometry.

Contribution

It introduces a method to construct quasi-convergent paths for blowup surfaces, expanding the noncommutative MMP framework and linking stability conditions with semiorthogonal decompositions.

Findings

Constructed a family of quasi-convergent paths for blowup surfaces.

Provided new semiorthogonal decompositions via parameter transformations.

Enhanced the noncommutative MMP approach for algebraic surfaces.

Abstract

We study the noncommutative minimal model program for blowups of surfaces. The program, as defined by Halpern-Leistner, is designed to construct a quasiconvergent path in the space of Bridgeland stability conditions. In this paper, we construct a family of quasi-convergent paths in the case of blowups of surfaces. These paths provide different semiorthogonal decompositions through parameter transformation.