On Cox rings of K3 surfaces
By M. Artebani, Jürgen Hausen, Antonio Laface. Compositio Mathematica, 2009
63 citations recorded by the source corpus.
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 rational 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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/99ec4c076cca9cec6e64ee87013a5d043978cd12
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Shinnosuke Okawa
- D. Huybrechts
- Alexander Kuznetsov
- E. Markman
- Kieran G. O’Grady
- P. Stellari
- Emanuele Macrì
- Keiji Oguiso
In Mathematical Physics
- Shinnosuke Okawa
- D. Huybrechts
- P. Stellari
- Emanuele Macrì
- E. Markman
- Keiji Oguiso
- Ulrike Riess
- D. Joyce
Citations in the corpus
- Lectures on K3 Surfaces (2016, methodology): “In fact, as shown by Artebani et al in [13] the Cox ring of a projective complex K3 surface is finitely generated if and only if NE(X) is rational polyhedral.”
- On images of Mori dream spaces (2011, background): “ them are toric varieties (and more generally spherical varieties [BK94]), varieties of Fano type in characteristic zero [BCHM10, Corollary 1.3.2], and K3 surfaces whose automorphism groups are finite [AHL10]. More generally, the cone conjecture asserts that Calabi-Yau varieties have similar structur”