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.

Export metadata

  • Export Bibtex
  • Export RIS

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Gert-Martin Greuel, Christop Lossen, Eugenii Shustin
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7487
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

$Rev: 12793 $