Journal of Commutative Algebra
- J. Commut. Algebra
- Volume 11, Number 2 (2019), 163-174.
The symmetric signature of cyclic quotient singularities
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.
J. Commut. Algebra, Volume 11, Number 2 (2019), 163-174.
First available in Project Euclid: 24 June 2019
Permanent link to this document
Digital Object Identifier
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.
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. https://projecteuclid.org/euclid.jca/1561363356