We study the shape of the F-signature function of a d-dimensional quotient singularity k〚x1,…,xd〛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⊆Gl(d,k). 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.

F-signature function of quotient singularities

Caminata, Alessio;De Stefani, Alessandro
2019

Abstract

We study the shape of the F-signature function of a d-dimensional quotient singularity k〚x1,…,xd〛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⊆Gl(d,k). 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/942106
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