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Exceptional curves on Del Pezzo surfaces

✍ Scribed by Andreas Leopold Knutsen

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 292 KB
Volume: 256
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310070

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✦ Synopsis

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 results of Pareschi [17] on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees ≥ 2 to the case of Del Pezzo surfaces of degree 1, where we explicitly classify the cases where the gonality and Clifford index are not constant.

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