Local Gromov-Witten invariants of some simple normal crossing surfaces

TL;DR

This paper extends the concept of local Gromov-Witten invariants from del Pezzo surfaces to a broader class of reducible surfaces with normal crossings, inspired by theoretical physics.

Contribution

It introduces a new framework for defining local Gromov-Witten invariants on shrinkable surfaces with normal crossings, expanding previous work on del Pezzo surfaces.

Findings

Defined local Gromov-Witten invariants for shrinkable surfaces

Extended invariants from smooth to reducible surfaces with normal crossings

Connected invariants to concepts in M-theory and superconformal field theory

Abstract

Inspired by M-theory and superconformal field theory, we extend the notions of local Gromov-Witten invariants from the case of del Pezzo surfaces to shrinkable surfaces, a class of reducible surfaces with simple normal crossings satisfying certain positivity conditions.