The higher rank local categorical DT/PT correspondence

TL;DR

This paper extends the local DT/PT correspondence to higher ranks using perverse coherent systems and quiver models, providing a categorical wallcrossing formula through semiorthogonal decompositions.

Contribution

It generalizes the categorical DT/PT correspondence to higher ranks and derives a new wallcrossing formula using advanced geometric and categorical techniques.

Findings

Derived higher rank local DT/PT models as critical loci.

Generalized categorical DT/PT correspondence to higher ranks.

Established categorical wallcrossing formula via semiorthogonal decompositions.

Abstract

In this paper we derive the higher rank local DT/PT models via the perverse coherent systems on the resolved conifold and the extended ADHM quiver, as critical loci. We generalize the categorical DT/PT correspondence by P\u{a}durariu and Toda to higher ranks and obtain the categorical wallcrossing formula as semiorthogonal decompositions.