Geometry of families of nodal curves on the blown-up projective plane
- Let P2r be the projective plane blown up at r generic points. Denote by E0; E1; : : : ; Er the strict transform of a generic straight line on P2 and the exceptional divisors of the blown-up points on P2r respectively. We consider the variety Virr of all irreducible curves C with k nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness, irreducibility and non-emptiness. Moreover, we extend our conditions for the smoothness and the irreducibility on families of reducible curves. For r ^ 9 we give the complete answer concerning the existence of nodal curves in Virr.
Author: | Gert-Martin Greuel, Christop Lossen, Eugenii Shustin |
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URN: | urn:nbn:de:hbz:386-kluedo-7487 |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1999 |
Year of first Publication: | 1999 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2000/04/03 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |