Geodesic
COX RINGS OF MINIMAL RESOLUTIONS OF SURFACE QUOTIENT SINGULARITIES
Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 325-355

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DOI

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. 
DONTEN-BURY, MARIA. COX RINGS OF MINIMAL RESOLUTIONS OF SURFACE QUOTIENT SINGULARITIES. Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 325-355. doi: 10.1017/S0017089515000221
@article{10_1017_S0017089515000221,
     author = {DONTEN-BURY, MARIA},
     title = {COX {RINGS} {OF} {MINIMAL} {RESOLUTIONS} {OF} {SURFACE} {QUOTIENT} {SINGULARITIES}},
     journal = {Glasgow mathematical journal},
     pages = {325--355},
     year = {2016},
     volume = {58},
     number = {2},
     doi = {10.1017/S0017089515000221},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000221/}
}
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