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Virtual Fundamental Classes of Zero Loci

2000/06/16 by David A. Cox, Sheldon Katz, Cox, David A. +3
Mathematics · #14D20 (Primary) #14N10 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D20 #msc:14N10

paper · pdf · doi:10.48550/arxiv.math/0006116

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

arxiv created 2000/12/06 · arxiv updated 2009/11/30

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.

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