F-signature function of quotient singularities

JOURNAL OF ALGEBRA

卷:523

Article

Caminata, Alessio¹  De Stefani, Alessandro² 

[1] Univ Barcelona, Inst Matemat, Gran Via Corts Catalanes 585, E-08007 Barcelona, Spain

[2] Univ Nebraska, Dept Math, 203 Avery Hall, Lincoln, NE 68588 USA

关键词: F-signature function;    Rings of invariants;    Finite small groups;    Frobenius endornorphism and;    F-singularities;    Veronese subrings;   

DOI  :  10.1016/j.jalgebra.2018.11.040

来源: Elsevier

【 摘 要 】

We study the shape of the F-signature function of a d-dimensional quotient singularity k[x(1), ..., x(d)](G), and we show that it is a quasi-polynomial. We prove that the second coefficient is always zero and we describe the other coefficients in terms of invariants of the finite acting group G subset of G1(d, k). When G is cyclic, we obtain more specific formulas for the coefficients of the quasi-polynomial, which allow us to compute the general form of the function in several examples. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free