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Computing the quantum cohomology of some Fano threefolds and its semisimplicity

Gianni Ciolli (2004)

Bollettino dell'Unione Matematica Italiana

We compute explicit presentations for the small Quantum Cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from P 3 or the smooth quadric. Systematic usage of the associativity property of quantum product implies that 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...

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