Cox rings of cubic surfaces and Fano threefolds

Abstract

We determine the Cox rings of the minimal resolutions of cubic surfaces with at most rational double points, of blow ups of the projective plane at non-general configurations of six points and of three dimensional smooth Fano varieties of Picard numbers one and two.

34 pages, section two expanded. To appear in Journal of Algebra

References in corpus (3)

• On G-Fano threefolds
• The density of rational points on Cayley's cubic surface
• On the Cox ring of blowing up the diagonal

Cited by in corpus (6)

• Iteration of Cox rings of klt singularities
• On smooth Fano fourfolds of Picard number two
• Projective and birational geometry of Grassmannians and other special varieties
• Integral points of bounded height on a log Fano threefold
• Spherical blow-ups of Grassmannians and Mori Dream Spaces
• The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one