Geometry of families of nodal curves on rational surfaces
| dc.creator | Greuel, Gert-Martin | |
| dc.creator | Lossen, Christoph | |
| dc.creator | Shustin, Eugenii | |
| dc.date | 1996-01-19 | |
| dc.date.accessioned | 2026-07-07T09:06:42Z | |
| dc.date.available | 2026-07-07T09:06:42Z | |
| dc.description | Let P^2_r be the projective plane blown up at r generic points. Denote by E_0,E_1,...,E_r the strict transform of a generic straight line on P^2 and the exceptional divisors of the blown-up points on P^2_r respectively. We consider the variety V of all irreducible curves C in |dE_0-d_1E_1-...-d_rE_r| with k nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness, irreducibility and non-emptyness. Moreover, we extend our conditions for the smoothness and the irreducibility on families of reducible curves. For r<10 we give the complete answer concerning the existence of nodal curves in V. | |
| dc.description | AMSLaTeX v 1.2 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9601020 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9601020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150104 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Geometry of families of nodal curves on rational surfaces | |
| dc.type | text |