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COX RINGS OF MINIMAL RESOLUTIONS OF SURFACE QUOTIENT SINGULARITIES

Part of: Special varieties Birational geometry Algebraic groups

Published online by Cambridge University Press:  21 July 2015

MARIA DONTEN-BURY
MARIA DONTEN-BURY*
Affiliation:
Instytut Matematyki UW, Banacha 2, PL-02097 Warsaw, Poland e-mail: M.Donten@mimuw.edu.pl
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Abstract

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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, which is a hypersurface in an affine space. The second is the set of generators of the Cox ring viewed as a subring of the coordinate ring of a product of a torus and another surface quotient singularity. In addition, we obtain an explicit description of the minimal resolution as a divisor in a toric variety.

MSC classification

Primary: 14E15: Global theory and resolution of singularities
Secondary: 14L30: Group actions on varieties or schemes (quotients) 14M25: Toric varieties, Newton polyhedra
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 325 - 355
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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