Characterization of varieties of Fano type via singularities of Cox rings

2012/01/05 by Gongyo, Yoshinori, Okawa, Shinnosuke, Sannai, Akiyoshi +1 · 3 citations
#14B05 #14E30 (Secondary) #14J45 (Primary) 13A35 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.1133

Abstract

We show that every Mori dream space of globally F-regular type is of Fano type. As an application, we give a characterization of varieties of Fano type in terms of the singularities of their Cox rings.

Cited by

• Fano compactifications of mutation algebras
• Free curves and fundamental groups
• On the uniform positivity of F-signature under reduction modulo p

Related

• Mori dream spaces of Calabi-Yau type and the log canonicity of the Cox rings
• Good quotients of Mori dream spaces
• Singularities of Cox Rings of Fano Varieties
• Hypersurfaces in Mori dream spaces
• Log Fano structures and Cox rings of blow-ups of products of projective spaces