Stable pair invariants on Calabi-Yau threefolds containing P^2

TL;DR

This paper establishes a relationship between stable pair invariants on certain Calabi-Yau threefolds and their derived orbifolds, revealing new constraints and connections via wall-crossing and theta series.

Contribution

It introduces a novel wall-crossing approach linking stable pair invariants on Calabi-Yau threefolds containing P^2 with those on derived equivalent orbifolds, involving generalized Donaldson-Thomas invariants.

Findings

Relation between stable pair invariants and orbifold invariants

Description of differences via theta series for indefinite lattices

Constraints among invariants caused by Seidel-Thomas twist

Abstract

We relate Pandharipande-Thomas stable pair invariants on Calabi-Yau 3-folds containing the projective plane with those on the derived equivalent orbifolds via wall-crossing method. The difference is described by generalized Donaldson-Thomas invariants counting semistable sheaves on the local projective plane, whose generating series form theta type series for indefinite lattices. Our result also derives non-trivial constraints among stable pair invariants on such Calabi-Yau 3-folds caused by Seidel-Thomas twist.