Multiple Cover Calculation for the Unramified Compactification of the Moduli Space of Stable Maps

TL;DR

This paper computes multiple cover Gromov-Witten integrals for the unramified compactification of the moduli space of stable maps to a specific embedded projective line in a Calabi-Yau threefold, extending known formulas.

Contribution

It introduces a calculation of multiple cover Gromov-Witten integrals for a new class of unramified compactifications in Calabi-Yau threefolds, generalizing the Aspinwall-Morrison formula.

Findings

Derived explicit formulas for multiple cover integrals.

Extended the Aspinwall-Morrison formula to new geometric settings.

Provided computational methods for unramified stable map moduli spaces.

Abstract

In this paper we compute the multiple cover Gromov-Witten integrals (analog of the Aspinwall-Morrison formula) for the unramified compactification of the moduli space of stable maps to an embedded $\PO$ in a Calabi-Yau threefold $X$ with the normal bundle $\mathcal{O}_{\PO}(-1) \bigoplus \mathcal{O}_{\PO}(-1)$.