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A McKay correspondence for the Poincaré series of some finite subgroups of SL3(C)

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Authors

  • Wolfgang Ebeling

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Details

Original languageEnglish
Article number19
Pages (from-to)397-408
Number of pages12
JournalJournal of Singularities
Volume18
Publication statusPublished - 2018

Abstract

A finite subgroup of SL2(C) defines a (Kleinian) rational surface singularity. The McKay correspondence yields a relation between the Poincaré series of the algebra of invariants of such a group and the characteristic polynomials of certain Coxeter elements determined by the corresponding singularity. Here we consider some non-abelian finite subgroups G of SL3(C). They define non-isolated three-dimensional Gorenstein quotient singularities. We consider suitable hyperplane sections of such singularities which are Kleinian or Fuchsian surface singularities. We show that we obtain a similar relation between the group G and the corresponding surface singularity.

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A McKay correspondence for the Poincaré series of some finite subgroups of SL3(C). / Ebeling, Wolfgang.
In: Journal of Singularities, Vol. 18, 19, 2018, p. 397-408.

Research output: Contribution to journal › Article › Research › peer review

Ebeling W. A McKay correspondence for the Poincaré series of some finite subgroups of SL3(C). Journal of Singularities. 2018;18:397-408. 19. doi: 10.5427/jsing.2018.18t
Ebeling, Wolfgang. / A McKay correspondence for the Poincaré series of some finite subgroups of SL3(C). In: Journal of Singularities. 2018 ; Vol. 18. pp. 397-408.
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