Mirror Principle I
Abstract
We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's 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 $¶^n$. This includes proving the formula of Candelasde la OssaGreenParkes hence completing the program of Candelas et al, Kontesevich, Manin, and Givental, to compute rigorously the instanton prepotential function for the quintic in $¶^4$. We derive, among many other examples, the multiple cover formula for GromovWitten invariants of $¶^1$, computed earlier by MorrisonAspinwall and by Manin in different approaches. We also prove a formula for enumerating Euler classes which arise in the socalled local mirror symmetry for some noncompact CalabiYau 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.
 Publication:

arXiv eprints
 Pub Date:
 December 1997
 arXiv:
 arXiv:alggeom/9712011
 Bibcode:
 1997alg.geom.12011L
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 Typos corrected, Plain Tex 50 pages with t.o.c option