Journal of Commutative Algebra

The symmetric signature of cyclic quotient singularities

Alessio Caminata and Lukas Katthan

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The symmetric signature is an invariant of local domains which was recently introduced by Brenner and the first author in an attempt to find a replacement for the $F$-signature in characteristic zero. In the present note we compute the symmetric signature for two-dimensional cyclic quotient singularities, i.e., invariant subrings $k[\mkern -2.75mu[ u,v]\mkern -2.75mu]^G$ of rings of formal power series under the action of a cyclic group. Equivalently, these rings arise as the completions (at the irrelevant ideal) of two-dimensional normal toric rings. We show that for this class of rings the symmetric signature coincides with the $F$-signature.

Article information

J. Commut. Algebra, Volume 11, Number 2 (2019), 163-174.

First available in Project Euclid: 24 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24] 52B20.

$F$-signature quotient singularity toric ring Auslander correspondence


Caminata, Alessio; Katthan, Lukas. The symmetric signature of cyclic quotient singularities. J. Commut. Algebra 11 (2019), no. 2, 163--174. doi:10.1216/JCA-2019-11-2-163.

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