Virtual Class of Zero Loci and Mirror Theorems

Artur Elezi

Virtual Class of Zero Loci and Mirror Theorems

Algebraic Geometry 2007-05-23 v2

Authors: Artur Elezi

Abstract

Let $Y$ be the zero loci of a regular section of a convex vector bundle $E$ over $X$ . We provide a new proof of a conjecture of Cox, Katz and Lee for the virtual class of the genus zero moduli of stable maps to $Y$ . This in turn yields the expected relationship between Gromov-Witten theories of $Y$ and $X$ which together with Mirror Theorems allows for the calculation of enumerative invariants of $Y$ inside of $X$ .

Keywords

vector bundles and cohomology moduli spaces of vector bundles vector bundles

Cite

@article{arxiv.math/0307386,
  title  = {Virtual Class of Zero Loci and Mirror Theorems},
  author = {Artur Elezi},
  journal= {arXiv preprint arXiv:math/0307386},
  year   = {2007}
}

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