# Multigraded Factorial Rings and Fano varieties with torus action

@article{Hausen2009MultigradedFR, title={Multigraded Factorial Rings and Fano varieties with torus action}, author={Juergen Hausen and Elaine Herppich and Hendrik Suss}, journal={arXiv: Algebraic Geometry}, year={2009} }

In a first result, we describe all finitely generated factorial algebras over an algebraically closed field of characteristic zero that come with an effective multigrading of complexity one by means of generators and relations. This enables us to construct systematically varieties with free divisor class group and a complexity one torus action via their Cox rings. For the Fano varieties of this type that have a free divisor class group of rank one, we provide explicit bounds for the number of…

## 25 Citations

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### COX RINGS OF MINIMAL RESOLUTIONS OF SURFACE QUOTIENT SINGULARITIES

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Abstract We investigate Cox rings of minimal resolutions of surface quotient singularities and provide two descriptions of these rings. The first one is the equation for the spectrum of a Cox ring,…

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Over the past several decades, toric geometry has become an increasingly important area of algebraic geometry. On the one hand, many deep theorems in algebraic geometry can be reduced to statements…

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We consider rational varieties with a torus action of complexity one and extend the combinatorial approach via the Cox ring developed for the complete case in earlier work to the non‐complete, e.g.…

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