Enumerating singular curves on surfaces
| dc.creator | Kleiman, Steven | |
| dc.creator | Piene, Ragni | |
| dc.date | 1999-03-31 | |
| dc.date | 2001-11-29 | |
| dc.date.accessioned | 2026-07-07T05:28:34Z | |
| dc.date.available | 2026-07-07T05:28:34Z | |
| dc.description | We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and up to three nodes. The curves must also pass through appropriately many general points. The number of curves is given by a universal polynomial in four basic Chern numbers. To justify the enumeration, we make a rudimentary classification of the types of singularities using Enriques diagrams, obtaining results like Arnold's. We show that the curves in question do, in fact, appear with multiplicity 1 using the versal deformation space, Shustin's codimension formula, and Gotzmann's regularity theorem. Finally, we relate our work to Vainsencher's work with up to seven nodes. | |
| dc.description | -- 31 pa ges, AMSTeX: revised version of the published article with minor corrections and updated references. -- 2 pages, plain TeX: correction sheet keyed to published version | |
| dc.identifier | https://arxiv.org/abs/math/9903192 | |
| dc.identifier | http://arxiv.org/abs/math/9903192 | |
| dc.identifier | Cont. Math. 241(1999), 209-239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78305 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14N10 (Primary); 14C20, 14H20 (Secondary) | |
| dc.title | Enumerating singular curves on surfaces | |
| dc.type | text |