Multiple cover formulas for abelian surfaces via correlated invariants

TL;DR

This paper proves the multiple cover formula conjecture for abelian surfaces, extending its validity to a broad class of invariants, including all stationary invariants, using advanced degeneration techniques.

Contribution

It introduces a proof of the multiple cover formula for abelian surfaces applicable to many invariants, utilizing correlated Gromov--Witten invariants and degeneration formulas.

Findings

Proves the multiple cover formula for abelian surfaces.

Validates the formula for all stationary invariants.

Uses reduced degeneration formula and correlated invariants.

Abstract

We prove the multiple cover formula conjecture for abelian surfaces for a large class of insertions, including all stationary invariants. The proof uses the reduced degeneration formula expressing the invariants in terms of the correlated Gromov--Witten invariants previously introduced by the authors.