Virtual Fundamental Classes of Zero Loci

Abstract

Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a conjecture which relates the virtual fundamental classes of X and Y. Using an argument due to Gathmann, we prove a special case of the conjecture. The paper concludes with a discussion of how our conjecture relates to the mirror theorems in the literature.

11 pages, Latex2e, using amsmath, amsfonts and amsthm packages. This revision includes minor revisions to the text and 4 new references