Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator
نویسندگان
چکیده
Quantum multiplications on the cohomology of symplectic manifolds were first proposed by the physicist Vafa [Va2] based on Witten’s topological sigma models [Wi1]. In [RuTi], Ruan and the second named author gave a mathematical construction of quantum multiplications on cohomology groups of positive symplectic manifolds (cf. Chapter 1). The construction uses the Gromov-Ruan-Witten invariants (GRW-invariants in the sequel) for semi-positive symplectic manifolds previously defined by Ruan [Ru]. A large class of such manifolds is provided by Fano manifolds (complex manifolds with ample anti-canonical bundle), including e.g. complex projective spaces, Del Pezzo surfaces and Grassmann manifolds. Let M be a Fano (or positive symplectic) manifold. The quantum cohomology
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