Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points

TL;DR

This paper derives virtual structure constants for mirror symmetry calculations using localization on moduli spaces of polynomial maps, simplifying computations for certain hypersurfaces and local geometries without Birkhoff factorization.

Contribution

It introduces a localization-based method to compute virtual structure constants directly from moduli spaces of polynomial maps, avoiding Birkhoff factorization.

Findings

Derived explicit formulas for virtual structure constants in hypersurface mirror symmetry.

Applied localization techniques to non-nef local geometries, expanding computational methods.

Demonstrated mirror computations without Birkhoff factorization, simplifying the process.

Abstract

In this paper, we derive the virtual structure constants used in mirror computation of degree k hypersurface in CP^{N-1}, by using localization computation applied to moduli space of polynomial maps from CP^{1} to CP^{N-1} with two marked points. We also apply this technique to non-nef local geometry O(1)+O(-3)->CP^{1} and realize mirror computation without using Birkhoff factorization.