On higher-dimensional del Pezzo varieties

Abstract

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.