Mukai Flop and Ruan Cohomology

Details Mukai Flop and Ruan Cohomology Mukai Flop and Ruan Cohomology

2003-02-03

arxiv.org/abs/math/0302022v2

Mathematics

Algebraic Geometry

Scientific paper

Suppose that two compact manifolds $X, X'$ are connected by a sequence of Mukai flops. In this paper, we construct a ring isomorphism between cohomology ring of $X$ and $X'$. Using the local mirror symmetry technique, we prove that the quantum corrected products on $X, X'$ are the ordinary intersection products. Furthermore, $X, X'$ have isomorphic Ruan cohomology. i.e. we proved the cohomological minimal model conjecture proposed by Ruan.

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