P-Divisors of Cox Rings

Details P-Divisors of Cox Rings P-Divisors of Cox Rings

2009-11-26

arxiv.org/abs/0911.5167v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

The Cox ring of a so-called Mori Dream Space (MDS) is finitely generated and it is graded over the divisor class group. Hence the spectrum of the Cox ring comes with an action of an algebraic torus whose GIT quotient is the variety in question. We present the associated description of this Cox ring as a polyhedral divisor. Via the shape of its polyhedral coefficients, it connects the equivariant structure of the Cox ring with the world of stable loci and stable multiplicities of linear systems.

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