On Cox rings of K3-surfaces

Abstract

We study Cox rings of K3-surfaces. A first result is that a K3-surface has a finitely generated Cox ring if and only if its effective cone is polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3-surfaces of Picard number two, and explicitly compute the Cox rings of generic K3-surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.

minor corrections, to appear in Compositio Mathematica, 32 pages

References in corpus (2)

• Sagbi Bases of Cox-Nagata Rings
• Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces

Cited by in corpus (21)

• On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32
• The Cox ring of an algebraic variety with torus action
• Characterization of varieties of Fano type via singularities of Cox rings
• An atlas of K3 surfaces with finite automorphism group
• Iteration of Cox rings of klt singularities
• Spherical blow-ups of Grassmannians and Mori Dream Spaces
• Mori dream spaces of Calabi-Yau type and the log canonicity of the Cox rings
• On minimal model theory for log abundant lc pairs
• Mori dream surfaces associated with curves with one place at infinity
• On images of Mori dream spaces
• A question of Doctor Malte Wandel on automorphisms of the punctural Hilbert schemes of K3 surfaces
• Geometric properties of projective manifolds of small degree
• Divisors on surfaces isogenous to a product of mixed type with $p_g=0$
• Birational geometry of blow-ups of projective spaces along points and lines
• On smooth Calabi-Yau threefolds of Picard number two
• Cox rings of K3 surfaces with Picard number two
• Good quotients of Mori dream spaces
• Examples of Mori dream surfaces of general type with $p_g=0$
• Cox rings of surfaces and the anticanonical Iitaka dimension
• Examples of Mori dream spaces with Picard number two
• The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces