TY - INPR
A1 - Greuel, Gert-Martin
A1 - Lossen, Christoph
A1 - Shustin, Eugenii
T1 - Castelnuvo Function, Zero-dimensional Schemes and Singular Plane Curves
N2 - 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 .
Y1 - 1999
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/782
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-7516
ER -