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 semisim...

In [1], Anscombe and Koenigsmann give an existential ∅-definition of the ring of formal power series F [[t]] in its quotient field in the case where F is finite. We extend their method in several directions to give general definability results for henselian valued fields with finite or pseudo-algebraically closed residue fields. §