Gorensteinness and iteration of Cox rings for Fano type varieties

2019/03/19 by Braun, Lukas · 1 citation
#13A02 #14J45 #14M05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.07996

Abstract

We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of Fano type and Kawamata log terminal quasicones, iteration of Cox rings is finite with factorial master Cox ring. Moreover, we prove a relative version of Cox ring iteration for almost principal solvable G-bundles.

Cited by

• Fano compactifications of mutation algebras

Related

• Singularities of Cox Rings of Fano Varieties
• On iteration of Cox rings
• Characterization of varieties of Fano type via singularities of Cox rings
• Equivariant Cox ring
• Log Fano structures and Cox rings of blow-ups of products of projective spaces