On the Quantum Cohomology of Some Fano Threefolds and a Conjecture of Dubrovin
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چکیده
In the present paper the small Quantum Cohomology ring of some Fano threefolds which are obtained as oneor two-curve blow-ups from P or the quadric Q is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov-Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of Quantum Cohomology is proven by checking the computed Quantum Cohomology rings and by showing that a smooth Fano threefold X with b3(X) = 0 admits a complete exceptional set of the appropriate length.
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تاریخ انتشار 2004