Finite generation of Cox rings
Algebraic Geometry
2022-10-03 v1 Commutative Algebra
Abstract
In this expository note we discuss a class of graded algebras named Cox rings, which are naturally associated to algebraic varieties generalizing the homogeneous coordinate rings of projective spaces. Whenever the Cox ring is finitely generated, the variety admits a quotient presentation by a quasitorus, which resembles the quotient construction of the projective space. We discuss the problem of the finite generation of Cox rings from a geometric perspective and provide examples of both the finitely and non-finitely generated cases.
Cite
@article{arxiv.2209.15633,
title = {Finite generation of Cox rings},
author = {José Luis González and Antonio Laface},
journal= {arXiv preprint arXiv:2209.15633},
year = {2022}
}
Comments
17 pages, 6 figures