On higher-dimensional del Pezzo varieties

DOI10.4213/IM9385EarXiv2206.01549MaRDI QIDQ6057089

Yuri G. Prokhorov, Alexander G. Kuznetsov

Publication date: 4 October 2023

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

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 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.

Full work available at URL: https://arxiv.org/abs/2206.01549

zbMATH Keywords

Fano varietyterminal singularitydel Pezzo variety

Mathematics Subject Classification ID

Rational and birational maps (14E05) Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30) Rationality questions in algebraic geometry (14E08)

Related Items (3)

Derived categories of Fano threefolds and degenerations ⋮ On maximally non-factorial nodal Fano threefolds ⋮ Some more Fano threefolds with a multiplicative Chow-Künneth decomposition

This page was built for publication: On higher-dimensional del Pezzo varieties