that their generating function is rational and satisfies an Igusa-type functional equation.

#### Acknowledgements

The work on this paper started at a Research in Pairs retreat at the Oberwolfach Forschunginstitute in 2014. We are grateful for the Institute for the ideal conditions. We would like to thank Alexander Beilinson, Bill Crawley-Boevey, Joel Kamnitzer, and Peng Shan for useful discussions. Special thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us. Research of T.H. was supported by the Advanced Grant “Arithmetic and physics of Higgs moduli spaces” no. 320593 of the European Research Council, by grants no. 144119, no. 153627 and NCCR SwissMAP, funded by the Swiss National Science Foundation. Research of E.L. was supported by ANR-13-BS01-0001-01.

Frobenius algebras {#Frobsection}
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Let $\k$ be field, which in this paper will be either finite or algebraically closed. Let $\R$ be a $\k$-algebra which is finite dimensional as a $\k$ vector space. We say that $\R$ is a Frobenius algebra if we have an $\R$-module isomorphism \_ \^[ \*]{},where $\R^*:=\operatorname{Hom}_\k(\R,\k)$ is an $\R$-module by $r\lambda(x)=\lambda(rx)$ for $\lambda\in\R^*$, $r,x\in \R$.

Equivalently to the condition a Frobenius algebra is defined by the 