Castelnuovo function, zero-dimensional schemes and singular plane curves

Details Castelnuovo function, zero-dimensional schemes and singular plane curves Castelnuovo function, zero-dimensional schemes and singular plane curves

1999-03-30

arxiv.org/abs/math/9903179v1

Mathematics

Algebraic Geometry

32 pages, 5 figures

Scientific paper

We study families V of curves in P^2 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 P^2. Moreover, we give a series of examples of cuspidal curves where the family V is reducible, but where the fundamental groups of P^2 \ C coincide (and are abelian) for all C in V.

Affiliated with

Also associated with

No associations

Rating

Castelnuovo function, zero-dimensional schemes and singular plane curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Castelnuovo function, zero-dimensional schemes and singular plane curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Castelnuovo function, zero-dimensional schemes and singular plane curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-660953