Stable pair invariants under blow-ups

TL;DR

This paper investigates how stable pair invariants of 3-folds change under blow-ups using degeneration formulas, providing new blow-up formulas and supporting the GW/DT/P correspondence.

Contribution

It introduces new closed-form blow-up formulas for stable pair invariants and discusses related Donaldson-Thomas invariants, extending the GW/DT/P correspondence.

Findings

Derived explicit blow-up formulas for stable pair invariants

Provided evidence supporting GW/DT/P correspondence

Extended results to non-toric, non-complete intersection varieties

Abstract

We use degeneration formula to study the change of stable pair invariants of 3-folds under blow-ups and obtain some closed blow-up formulae. Related results on Donaldson-Thomas invariants are also discussed. Our results give positive evidence for GW/DT/P correspondence, and also give partial correspondence for varieties not necessarily toric or complete intersections.