On factoriality of Cox rings
Algebraic Geometry
2009-08-22 v1 Commutative Algebra
Abstract
Generalized Cox's construction associates with an algebraic variety a remarkable invariant -- its total coordinate ring, or Cox ring. In this note we give a new proof of factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on a notion of graded factoriality. We show that if the divisor class group has torsion, then the Cox ring is again factorially graded, but factoriality may be lost.
Cite
@article{arxiv.0802.0763,
title = {On factoriality of Cox rings},
author = {Ivan V. Arzhantsev},
journal= {arXiv preprint arXiv:0802.0763},
year = {2009}
}
Comments
7 pages