Mirror Maps, Modular Relations and Hypergeometric Series I

Abstract

Motivated by the recent work of Kachru-Vafa in string theory, we study in Part A of this paper, certain identities involving modular forms, hypergeometric series, and more generally series solutions to Fuchsian equations. The identity which arises in string theory is the simpliest of its kind. There are nontrivial generalizations of the identity which appear new. We give many such examples -- all of which arise in mirror symmetry for algebraic K3 surfaces. In Part B, we study the integrality property of certain $q$-series, known as mirror maps, which arise in mirror symmetry.

24 pages; harvmac

Cited by in corpus (4)

• Geometric Engineering of Quantum Field Theories
• New Higgs Transitions between Dual N=2 String Models
• Criterion for the integrality of the Taylor coefficients of mirror maps in several variables
• Schwarzian conditions for linear differential operators with selected differential Galois groups (unabridged version)