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

Abstract

In this paper, we derive the virtual structure constants used in the mirror computation of the degree k hypersurface in CP N-1, by using a localization computation applied to moduli space of polynomial maps from CP 1 to CP N-1 with two marked points. This moduli space corresponds to the GIT quotient of the standard moduli space of instantons of Gauged Linear Sigma Model by the standard torus action. We also apply this technique to the non-nef local geometry $${{\cal O}(1)\oplus {\cal O}(-3)\rightarrow CP^{1}}$$ and realize the mirror computation without using Birkhoff factorization. Especially, we obtain a geometrical construction of the expansion coefficients of the mirror maps of these models.