Rational surfaces in P^4 containing a plane curve
| dc.creator | Catanese, Fabrizio | |
| dc.creator | Hulek, Klaus | |
| dc.date | 1995-05-23 | |
| dc.date.accessioned | 2026-07-07T09:06:30Z | |
| dc.date.available | 2026-07-07T09:06:30Z | |
| dc.description | The families of smooth rational surfaces in $\PP^4$ have been classified in degree $\le 10$. All known rational surfaces in $\PP^4$ can be represented as blow-ups of the plane $\PP^2$. The fine classification of these surfaces consists of giving explicit open and closed conditions which determine the configurations of points corresponding to all surfaces in a given family. Using a restriction argument originally due independently to Alexander and Bauer we achieve the fine classification in two cases, namely non-special rational surfaces of degree 9 and special rational surfaces of degree 8. The first case completes the fine classification of all non-special rational surfaces. In the second case we obtain a description of the moduli space as the quotient of a rational variety by the symmetric group $S_5$. We also discuss in how far this method can be used to study other rational surfaces in $\PP^4$. | |
| dc.description | 25 pages, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9505021 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9505021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150032 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Rational surfaces in P^4 containing a plane curve | |
| dc.type | text |