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arXiv · 1603.06427

The Symmetric signature of cyclic quotient singularities

Alessio Caminata·Lukas Katthän
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Abstract

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 $k[[u,v]]^G$ of rings of formal power series under the action of a cyclic group $G$. 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.

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Alessio Caminata, Lukas Katthän. 2016-03-21. The Symmetric signature of cyclic quotient singularities. https://doi.org/10.1216/jca-2019-11-2-163

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