Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kähler Forms

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 Kähler 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.

45 pages, 2 figures, minor errors are corrected, English is refined. Section 1 and Section 2 are enlarged. Especially in Section 2, confusion between the notion of resolution and the notion of compactification is resolved. Computation under non-zero equivariant parameters are added in Section2

References in corpus (1)

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

Cited by in corpus (11)

• Multi-Point Virtual Structure Constants and Mirror Computation of CP^2-model
• Wall-crossing in genus zero quasimap theory and mirror maps
• Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
• Geometrical Proof of Generalized Mirror Transformation of Projective Hypersurfaces
• Moduli Space of Quasi-Maps from P^{1} with Two Marked Points to P(1,1,1,3) and j-invariant
• Elliptic Virtual Structure Constants and Generalizations of BCOV-Zinger Formula to Projective Fano Hypersurfaces
• Generalized Hypergeometric Functions for Degree k Hypersurface in CP^{N-1} and Intersection Numbers of Moduli Space of Quasimaps from CP^{1} with Two Marked Points to CP^{N-1}
• Chow Rings of Mp_{0,2}(N,d) and Mbar_{0,2}(P^{N-1},d) and Gromov-Witten Invariants of Projective Hypersurfaces of Degree 1 and 2
• Classical Computation of Number of Lines in Projective Hypersurfaces: Origin of Mirror Transformation
• Period Integrals (Givental's I-function) of Calabi-Yau Hypersurface in $C{P}^{N-1}$ and Intersection Numbers of Moduli Space of Quasimaps from $C{P}^1$ with Two Marked Points to $C{P}^{N-1}$
• Toric Construction and Chow Ring of Moduli Space of Quasi Maps from ${\mathbb{P}}^1$ with Two Marked Points to ${\mathbb{P}}^1\times {\mathbb{P}}^1$