Singularities of Cox Rings of Fano Varieties

2011/09/28 by Morgan V. Brown, Brown, Morgan V.
Mathematics · #14C20 #14J45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1109.6368

openalex publication_date 2011/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth complete Fano variety over ℂ. We show that the Cox ring \bigoplus_L\inPic(X)H⁰(X,O_X(L)) is Gorenstein with canonical singularities.

Related

• Gorensteinness and iteration of Cox rings for Fano type varieties
• Characterization of varieties of Fano type via singularities of Cox rings
• The Cox Ring of a Del Pezzo Surface Has Rational Singularities
• Singularities of pluri-fundamental divisors on Gorenstein Fano varieties of coindex 4
• On the anti-canonical ring and varieties of Fano type