Mukai Flop and Ruan Cohomology

Jianxun Hu; Wanchuan Zhang

Mukai Flop and Ruan Cohomology

Algebraic Geometry 2007-05-23 v2 Symplectic Geometry

Authors: Jianxun Hu , Wanchuan Zhang

Abstract

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.

Keywords

mukai flop ruan cohomology cohomology ring quantum corrected product local mirror symmetry minimal model conjecture

Cite

@article{arxiv.math/0302022,
  title  = {Mukai Flop and Ruan Cohomology},
  author = {Jianxun Hu and Wanchuan Zhang},
  journal= {arXiv preprint arXiv:math/0302022},
  year   = {2007}
}

Mukai Flop and Ruan Cohomology

Abstract

Keywords

Cite

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