Counting Curves with Modular Forms

Abstract

We consider the type IIA string compactified on the Calabi-Yau space given by a degree 12 hypersurface in the weighted projective space ${\mathbf{P}}_{(1,1,2,2,6)}^4$. We express the prepotential of the low-energy effective supergravity theory in terms of a set of functions that transform covariantly under $PSL(2,\mathbb{Z})$ modular transformations. These functions are then determined by monodromy properties, by singularities at the massless monopole point of the moduli space, and by $S\leftrightarrow T$ exchange symmetry.

Minor changes, added references, 12 pages, uses harvmac

References in corpus (12)

• Exact Results for N=2 Compactifications of Heterotic Strings
• Algebras, BPS States, and Strings
• Nonperturbative Results on the Point Particle Limit of N=2 Heterotic String Compactifications
• K3--Fibrations and Heterotic-Type II String Duality
• Second-Quantized Mirror Symmetry
• Perturbative Couplings of Vector Multiplets in $N=2$ Heterotic String Vacua
• On the Ubiquity of K3 Fibrations in String Duality
• Aspects of Duality in N=2 String Vacua
• Perturbative Prepotential and Monodromies in N=2 Heterotic Superstring
• BPS Spectra and Non--Perturbative Couplings in N=2,4 Supersymmetric String Theories
• Duality Symmetries in N=2 Heterotic Superstring
• K3 surfaces, Lorentzian Kac--Moody algebras and Mirror Symmetry

Cited by in corpus (9)

• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• (0,2) Heterotic Gauge Couplings and their M-Theory Origin
• Holomorphic Couplings in String Theory
• A lecture on Arithmetic Mirror Symmetry and Calabi-Yau manifolds
• Quantum N = 2 Supersymmetric Black Holes in the S-T Model
• Borcherds Algebras and N=4 Topological Amplitudes
• On quantum corrected Kähler potentials in F-theory
• Special Geometry and Automorphic Forms