On the Quantum Cohomology of some Fano threefolds and a conjecture of Dubrovin
| dc.creator | Ciolli, Gianni | |
| dc.date | 2004-03-18 | |
| dc.date | 2004-03-23 | |
| dc.date.accessioned | 2026-07-07T05:06:31Z | |
| dc.date.available | 2026-07-07T05:06:31Z | |
| dc.description | In 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.description | 15 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.identifier | https://arxiv.org/abs/math/0403300 | |
| dc.identifier | http://arxiv.org/abs/math/0403300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70499 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14N35 (Primary); 14J45 (Secondary) | |
| dc.title | On the Quantum Cohomology of some Fano threefolds and a conjecture of Dubrovin | |
| dc.type | text |