On the Quantum Cohomology of some Fano threefolds and a conjecture of Dubrovin

dc.creatorCiolli, Gianni
dc.date2004-03-18
dc.date2004-03-23
dc.date.accessioned2026-07-07T05:06:31Z
dc.date.available2026-07-07T05:06:31Z
dc.descriptionIn the present paper the small Quantum Cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from $P^3$ or the quadric $Q^3$ 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 $b_3(X)=0$ admits a complete exceptional set of the appropriate length.
dc.description15 pages, 3 tables. In v2 two small mistakes were corrected: a missing hypothesis in the citation of Theorem 6 and a wrong bibliographic citation
dc.identifierhttps://arxiv.org/abs/math/0403300
dc.identifierhttp://arxiv.org/abs/math/0403300
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70499
dc.subjectAlgebraic Geometry
dc.subject14N35 (Primary); 14J45 (Secondary)
dc.titleOn the Quantum Cohomology of some Fano threefolds and a conjecture of Dubrovin
dc.typetext

Files

Collections