Reduced invariants from cuspidal maps

TL;DR

This paper establishes a connection between genus 1 enumerative invariants from a specific moduli space and Vakil-Zinger reduced invariants for the quintic threefold, offering a new modular interpretation.

Contribution

It demonstrates that invariants from Smyth-Viscardi moduli space coincide with Vakil-Zinger reduced invariants, providing a novel modular perspective.

Findings

Invariants from Smyth-Viscardi moduli space match Vakil-Zinger reduced invariants

Provides a modular interpretation for Vakil-Zinger invariants

Establishes equivalence for genus 1 enumerative invariants in this context

Abstract

We consider genus 1 enumerative invariants arising from the Smyth-Viscardi moduli space of stable maps from curves with nodes and cusps. We prove that these invariants are equal to the Vakil-Zinger reduced invariants for the quintic threefold, providing a modular interpretation of the latter.