Singular symplectic flops and Ruan cohomology

ar X iv : 0 80 4 . 31 44 v 1 [ m at h . SG ] 1 9 A pr 2 00 8 SINGULAR SYMPLECTIC FLOPS AND RUAN COHOMOLOGY

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient Wr = {(x, y, z, t)|xy − z + t = 0}/μr(a,−a, 1, 0), r ≥ 1, which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let X and Y be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of...

The Intersection Cohomology of Singular Symplectic Quotients

We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That i...

Mukai Flop and Ruan Cohomology

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 localization 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 ...

Notes on Chen-ruan Cohomology

Chen–ruan Cohomology of Some Moduli Spaces

Let X be a compact connected Riemann surface of genus at least two. We compute the Chen–Ruan cohomology ring of the moduli space of stable PSL(2, C)– bundles of nontrivial second Stiefel–Whitney class over X .