Blow-up formulae of high genus Gromov-Witten invariants in dimensional six

TL;DR

This paper derives explicit blow-up formulae for high genus Gromov-Witten invariants in six-dimensional symplectic manifolds, revealing relations with generalized BPS numbers and advancing understanding of their behavior under geometric transformations.

Contribution

It provides the first closed-form blow-up formulae for high genus Gromov-Witten invariants in six dimensions, utilizing degeneration and absolute/relative correspondence techniques.

Findings

Derived explicit blow-up formulae for high genus invariants

Established relations among generalized BPS numbers

Enhanced understanding of invariants' behavior under blow-up

Abstract

Using the degeneration formula and absolute/relative correspondence, one studied the change of Gromov-Witten invariants under blow-up for six dimensional symplectic manifolds and obtained closed blow-up formulae for high genus Gromov-Witten invariants. Our formulae also imply some relations among generalized BPS numbers introduced by Pandharipande.