منابع مشابه
Cox Rings and Combinatorics Ii
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...
متن کاملDivisorial 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...
متن کامل2 5 Ja n 20 08 COX RINGS AND COMBINATORICS II
We study varieties with a finitely generated Cox ring. In a 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 mo...
متن کاملUniversal Torsors and Cox Rings
— We study the equations of universal torsors on rational surfaces.
متن کاملOn Factoriality of Cox Rings
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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2006
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-06-03904-3