## Abstract We classify all cases of exceptional curves on Del Pezzo surfaces, which turn out to be the smooth plane curves and some other cases with Clifford dimension 3. Moreover, the property of being exceptional holds for all curves in the complete linear system. We use this study to extend the
On non-normal del Pezzo surfaces
β Scribed by Makoto Abe; Mikio Furushima
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 178 KB
- Volume
- 260
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let Y be a nonβnormal del Pezzo surface over β and let d β (Ο^β1^~Y~)^2^ > 0 be the degree of Y. Then we prove that Ο^βdβ4^~Y~ is very ample for d = 1, 2.
π SIMILAR VOLUMES
A k-very ample line bundle L on a Del Peaao Surface is numerically characterized, improving the results of BIANCOFIOR.E -CERESA in [7]. ample line bundles on surfaces whose Picard group is fully known. k -very ample line bundles on P2, on the Hirzebruch surfaces Fn and on hyperelliptic surfaces are
The automorphism group of a generic quartic del Pezzo surface is isomorphic to Ε½ . 4 w Ε½ . x the group β«ή2βͺrβ¬ήβ¬ M. Koitabashi, J. Algebra 116 1988 , 130α142 . In this article, we determine the automorphism group of each quartic del Pezzo surface.
## Abstract Let __L__ be a nef line bundle on a Del Pezzo surface. We show that __L__ + __K~S~__ is birationally __k__βvery ample if and only if all the smooth curves in |__L__| have gonality β₯__k__ + 2, and we also find numerical criteria for birational __k__βvery ampleness.