Virtual Class of Zero Loci and Mirror Theorems

Details Virtual Class of Zero Loci and Mirror Theorems Virtual Class of Zero Loci and Mirror Theorems

2003-07-30

arxiv.org/abs/math/0307386v2

Adv. Theor. Math. Phys. 7 (2004) 1103-1116

Mathematics

Algebraic Geometry

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Scientific paper

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 $X$.

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