Mirror principle I

Abstract

We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of obstruction bundles induced by any concavex bundles -including any direct sum of line bundles -on P n . This includes proving the formula of Candelas-de la Ossa-Green-Parkes for the instanton prepotential function for quintic in P 4 . We derive, among many other examples, the so-called multiple cover formula for GW invariants of P 1 . We also prove a formula for enumerating Euler classes which arise in the so-called local mirror symmetry for some noncompact Calabi-Yau manifolds. At the end we interprete an infinite dimensional transformation group, called the mirror group, acting on Euler data, as a certain duality group of the linear sigma model.