A McKay correspondence for the Poincaré series of some finite subgroups of SL_3(C)
Journal of Singularities, Tome 18 (2018), pp. 397-408
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A finite subgroup of SL_2(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 SL_3(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.
@article{10_5427_jsing_2018_18t,
author = {Wolfgang Ebeling},
title = {A {McKay} correspondence for the {Poincar\'e} series of some finite subgroups of {SL_3(C)}},
journal = {Journal of Singularities},
pages = {397--408},
publisher = {mathdoc},
volume = {18},
year = {2018},
doi = {10.5427/jsing.2018.18t},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.18t/}
}
TY - JOUR AU - Wolfgang Ebeling TI - A McKay correspondence for the Poincaré series of some finite subgroups of SL_3(C) JO - Journal of Singularities PY - 2018 SP - 397 EP - 408 VL - 18 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.18t/ DO - 10.5427/jsing.2018.18t ID - 10_5427_jsing_2018_18t ER -
%0 Journal Article %A Wolfgang Ebeling %T A McKay correspondence for the Poincaré series of some finite subgroups of SL_3(C) %J Journal of Singularities %D 2018 %P 397-408 %V 18 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.18t/ %R 10.5427/jsing.2018.18t %F 10_5427_jsing_2018_18t
Wolfgang Ebeling. A McKay correspondence for the Poincaré series of some finite subgroups of SL_3(C). Journal of Singularities, Tome 18 (2018), pp. 397-408. doi: 10.5427/jsing.2018.18t
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