Hilbert scheme of points on cyclic quotient singularities of type (p, 1)
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In this note we investigate the generating series of the Euler characteristics of the Hilbert scheme of points on cyclic quotient singularities of type (p, 1). We link the appearing combinatorics to p-fountains, a generalization of the notion of fountain of coins. We obtain a representation of the generating series as a coefficient of a two variable generating series.
KeywordsHilbert scheme Cyclic quotient singularity p-fountain
The author thanks to András Némethi for fruitful conversations about the problem. The author was partially supported by the Lendület program of the Hungarian Academy of Sciences and by the ERC Advanced Grant LDTBud (awarded to András Stipsicz).
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