Advances in Theoretical and Mathematical Physics

Volume 7 (2003)

Number 6

Virtual class of zero loci and mirror theorems

Pages: 1103 – 1115

DOI: http://dx.doi.org/10.4310/ATMP.2003.v7.n6.a5

Authors

Artur Elezi

Feng Luo

Abstract

Let $Y$ be the zero loci of a regular section of a convex vector bundle $E$ over $X$. We provide a 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 $X$.

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