Castelnuovo function, zero-dimensional schemes and singular plane curves
| dc.creator | Greuel, Gert-Martin | |
| dc.creator | Lossen, Christoph | |
| dc.creator | Shustin, Eugenii | |
| dc.date | 1999-03-30 | |
| dc.date.accessioned | 2026-07-07T05:28:32Z | |
| dc.date.available | 2026-07-07T05:28:32Z | |
| dc.description | 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. | |
| dc.description | 32 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/9903179 | |
| dc.identifier | http://arxiv.org/abs/math/9903179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78295 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H15;14H20;14C05 | |
| dc.title | Castelnuovo function, zero-dimensional schemes and singular plane curves | |
| dc.type | text |