Premium
Exceptional curves on Del Pezzo surfaces
Author(s) -
Knutsen Andreas Leopold
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310070
Subject(s) - mathematics , dimension (graph theory) , degree (music) , constant (computer programming) , pure mathematics , mathematical analysis , property (philosophy) , plane (geometry) , geometry , philosophy , physics , epistemology , computer science , acoustics , programming language
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.