Mirror principle I

We propose and study the following Mirror Principle: certain sequences of m ultiplicative equivariant characteristic classes on stable map moduli space s can be computed in terms of certain hypergeometric type classes. As appli cations, we compute the equivariant Euler classes of obstruction bundles in duced 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-Park es for the instanton prepotential function for quintic in P-4. We derive, a mong many other examples, the so-called multiple cover formula for GW invar iants of P-1. We also prove a formula for enumerating Euler classes which a rise 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.