Degenerating curves and surfaces: first results
| dc.creator | Galati, Concettina | |
| dc.date | 2008-10-01 | |
| dc.date | 2009-03-20 | |
| dc.date.accessioned | 2026-07-07T12:54:08Z | |
| dc.date.available | 2026-07-07T12:54:08Z | |
| dc.description | Let $\mathcal S\to\mathbb A^1$ be a smooth family of surfaces whose general fibre is a smooth surface of $\mathbb P^3$ and whose special fibre has two smooth components, intersecting transversally along a smooth curve $R$. We consider the Universal Severi-Enriques variety $\mathcal V$ on $\mathcal S\to\mathbb A^1$. The general fibre of $\mathcal V$ is the variety of curves on $\mathcal S_t$ in the linear system $|\mathcal O_{\mathcal S_t}(n)|$ with $k$ cusps and $δ$ nodes as singularities. Our problem is to find all irreducible components of the special fibre of $\mathcal V$. In this paper, we consider only the cases $(k,δ)=(0,1)$ and $(k,δ)=(1,0)$. In particular, we determine all singular curves on the special fibre of $\mathcal S$ which, counted with the right multiplicity, are a limit of 1-cuspidal curves on the general fibre of $\mathcal S$. | |
| dc.description | 24 pages; minor changes | |
| dc.identifier | https://arxiv.org/abs/0810.0105 | |
| dc.identifier | http://arxiv.org/abs/0810.0105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223823 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H15; 14H10; 14B05 | |
| dc.title | Degenerating curves and surfaces: first results | |
| dc.type | text |