Mirror symmetry for concavex vector bundles on projective spaces

Details Mirror symmetry for concavex vector bundles on projective spaces Mirror symmetry for concavex vector bundles on projective spaces

2000-04-25

arxiv.org/abs/math/0004157v2

International Journal of Mathematics and Mathematical Sciences (2003), no. 3, 159-197

Mathematics

Algebraic Geometry

35 pages, LaTeX2e. Several minor errors have been corrected

Scientific paper

Let $X\subset Y$ be smooth, projective manifolds. Assume that $X$ is the zero locus of a generic section of a direct sum $V+$ of positive line bundles on $\PP^n$. Furthermore assume that the normal bundle $N_{X/Y}$ is a direct sum $V-$ of negative line bundles. We show that a $V:=V+\oplus V-$-twisted Gromov-Witten theory of $\PP^n$ restricts to the Gromov-Witten theory of $X$ inherited form $Y$. The later one can be computed via a Mirror Theorem which we prove in this paper.

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