Computing resolutions of quotient singularities

JOURNAL OF ALGEBRA

卷:472

Article

Donten-Bury, Maria^1,2  Keicher, Simon³ 

[1] Univ Warsaw, Inst Math, Banacha 2, PL-02097 Warsaw, Poland

[2] Free Univ Berlin, Inst Math, Arnimallee 3, D-14195 Berlin, Germany

[3] Univ Concepcion, Fac Ciencias Fis & Matemat, Dept Matemat, Casilla 160-C, Concepcion, Chile

关键词: Cox ring;    Resolution of singularities;    Quotient singularity;    Mori dream space;   

DOI  :  10.1016/j.jalgebra.2016.10.042

来源: Elsevier

【 摘 要 】

Let G subset of GL(n) be a finite group without pseudo-reflections. We present an algorithm to compute and verify a candidate for the Cox ring of a resolution X -> 4 C-n/G, which is based just on the geometry of the singularity C-n/G, without further knowledge of its resolutions. We explain the use of our implementation of the algorithms in Singular. As an application, we determine the Cox rings of resolutions X -> C-3/G for all G subset of GL(3) with the aforementioned property and of order vertical bar G vertical bar <= 12. We also provide examples in dimension 4. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free