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arXiv · 1804.01281

F-signature function of quotient singularities

Alessio Caminata·Alessandro De Stefani
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Abstract

We study the shape of the F-signature function of a $d$-dimensional quotient singularity $\mathbb{k}[[ x_1,\ldots,x_d]]^G$, 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 $G\subseteq \mathrm{Gl}(d,\Bbbk)$. 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.

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Alessio Caminata, Alessandro De Stefani. 2018-05-09. F-signature function of quotient singularities. https://arxiv.org/abs/1804.01281

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