Castelnuvo Function, Zero-dimensional Schemes and Singular Plane Curves

  • We study families V of curves in P2(C) of degree d having exactly r singular points of given topological or analytic types. We derive new sufficient conditions for V to be T-smooth (smooth of the expected dimension), respectively to be irreducible. For T-smoothness these conditions involve new invariants of curve singularities and are conjectured to be asymptotically proper, i.e., optimal up to a constant factor. To obtain the results, we study the Castelnuovo function, prove the irreducibility of the Hilbert scheme of zero-dimensional schemes associated to a cluster of infinitely near points of the singularities and deduce new vanishing theorems for ideal sheaves of zero-dimensional schemes in P2. Moreover, we give a series of examples of cuspidal curves where the family V is reducible, but where ss1(P2nC) coincides (and is abelian) for all C 2 V .

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Author:Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7516
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

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