Geometry of families of nodal curves on rational surfaces

dc.creatorGreuel, Gert-Martin
dc.creatorLossen, Christoph
dc.creatorShustin, Eugenii
dc.date1996-01-19
dc.date.accessioned2026-07-07T09:06:42Z
dc.date.available2026-07-07T09:06:42Z
dc.descriptionLet 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.descriptionAMSLaTeX v 1.2
dc.identifierhttps://arxiv.org/abs/alg-geom/9601020
dc.identifierhttp://arxiv.org/abs/alg-geom/9601020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150104
dc.subjectAlgebraic Geometry
dc.titleGeometry of families of nodal curves on rational surfaces
dc.typetext

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