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.
"The symmetric signature of cyclic quotient singularities." J. Commut. Algebra 11 (2) 163 - 174, 2019. https://doi.org/10.1216/JCA-2019-11-2-163