Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two K\"ahler Forms

TL;DR

This paper extends the geometric derivation of mirror map expansion coefficients to toric manifolds with two K"ahler forms, using localization computations, with specific examples like Hirzebruch surfaces and Calabi-Yau hypersurfaces.

Contribution

It introduces a method to compute mirror map coefficients for toric manifolds with multiple K"ahler forms, expanding previous approaches to more complex geometries.

Findings

Derived mirror map expansion coefficients for specific toric manifolds.

Demonstrated the method on Hirzebruch surfaces and Calabi-Yau hypersurfaces.

Results suggest generalization to arbitrary toric manifolds.

Abstract

In this paper, we extend our geometrical derivation of expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples. We expect that our results can be easily generalized to arbitrary toric manifold.