Computing Cox rings
نویسندگان
چکیده
منابع مشابه
Divisorial rings and Cox rings
1 Preliminaries on monoids Definition 1.1. An Abelian monoid is a set with a binary, associative, and commutative operation which has a neutral element. It will often be called just a monoid in this manuscript because we will not deal with non-commutative monoids. A monoid M is called • finitely generated if there is a finite set of generators, or equivalently if there is a surjection of monoid...
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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 ri...
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We study varieties with a finitely generated Cox ring. In the first part, we generalize a combinatorial approach developed in earlier work for varieties with a torsion free divisor class group to the case of torsion. Then we turn to modifications, e. g., blow-ups, and the question how the Cox ring changes under such maps. We answer this question for a certain class of modifications induced from...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2015
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/2989