# Curves and line bundles on Del Pezzo surfaces

@inproceedings{Knutsen2001CurvesAL, title={Curves and line bundles on Del Pezzo surfaces}, author={Andreas Leopold Knutsen}, year={2001} }

We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ 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. We also 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… CONTINUE READING

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