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- Title
A geometric criterion for the finite generation of the Cox rings of projective surfaces.
- Authors
De La Rosa Navarro, Brenda Leticia; Medina, J. Bosco Frıas; Lahyane, Mustapha; Mejıa, Israel Moreno; Castro, Osvaldo Osuna
- Abstract
The aim of this paper is to give a geometric characterization of the finite generation of the Cox rings of anticanonical rational surfaces. This characterization is encoded in the finite generation of the effective monoid. Furthermore, we prove that in the case of a smooth projective rational surface having a negative multiple of its canonical divisor with only two linearly independent global sections (e.g., an elliptic rational surface), the finite generation is equivalent to the fact that there are only a finite number of smooth projective rational curves of self-intersection-1. The ground field is assumed to be algebraically closed of arbitrary characteristic.
- Subjects
GEOMETRY; MODULES (Algebra); PROJECTIVE modules (Algebra); ALGEBRA; RING theory; RING extensions (Algebra)
- Publication
Revista Mathematica Iberoamericana, 2015, Vol 31, Issue 4, p1131
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/878