Semiorthogonal decompositions of projective spaces from small quantum cohomology

TL;DR

This paper explores the construction of semiorthogonal decompositions of derived categories of projective spaces via quasi-convergent paths in the stability manifold, linking stability conditions with quantum cohomology.

Contribution

It demonstrates the existence of quasi-convergent paths originating from geometric regions with central charges related to quantum differential equations and quantum cohomology.

Findings

Constructed quasi-convergent paths from geometric regions.

Linked stability conditions with quantum differential equations.

Connected quantum cohomology central charges to stability paths.

Abstract

In a recent article Halpern-Leistner defines the notion of quasi--convergent path in the space of Bridgeland stability conditions. Such a path induces a semiorthogonal decomposition of the derived category. We investigate quasi-convergent paths in the stability manifold of projective spaces and answer positively to two questions posed by Halpern-Leistner. We construct quasi-convergent paths that start from the geometric region of the stability space and whose central charge is given by a fundamental solution of the quantum differential equation. We also construct quasi-convergent paths whose central charges are the quantum cohomology central charges defined by Iritani.