On higher-dimensional del~Pezzo varieties

A. G. Kuznetsov ; Yu. G. Prokhorov

Izvestiya. Mathematics , Tome 87 (2023) no. 3, pp. 488-561.

Résumé

We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type $\mathrm A$ the dimension of non-conical del Pezzo varieties is bounded by $12 - d - r$, where $d$ is the degree and $r$ is the rank of the class group, and classify maximal del Pezzo varieties.

Détail

Keywords: Fano variety, del Pezzo variety, terminal singularity.

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