On higher-dimensional del Pezzo varieties

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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.

About the authors

Alexander Gennad'evich Kuznetsov

Steklov Mathematical Institute of Russian Academy of Sciences; Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE)

Email: akuznet@mi-ras.ru
Doctor of physico-mathematical sciences, no status

Yuri Gennadievich Prokhorov

Steklov Mathematical Institute of Russian Academy of Sciences; Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE)

Email: prokhoro@mi-ras.ru
Doctor of physico-mathematical sciences, Professor

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