Del Pezzo surfaces with log-terminal singularities.~II

V. V. Nikulin

Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 355-372.

Résumé

If $Z$ is a del Pezzo surface with log-terminal singularities of index dividing $k$ and $\sigma\colon Y\to Z$ the minimal resolution of singularities of $Z$, we prove the inequality $\operatorname{rk\,Pic}Y$, where $A$ is an absolute constant. It follows from this that for fixed $k$ there are only a finite number of possible intersection graphs of all exponential curves on $Y$. In Part I these results were obtained under a certain restriction on the singularities. The proof uses methods taken from the theory of reflection groups in Lobachevsky space. Bibliography: 14 titles.

Bibliographie

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[12] Nikulin V. V., Poverkhnosti del Petstso s log-terminalnymi osobennostyami. Algebraicheskaya geometriya, Dep. v VINITI, 1988

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