Zeta functions of groups - singular Pfaffians

Details Zeta functions of groups - singular Pfaffians Zeta functions of groups - singular Pfaffians

2003-09-30

arxiv.org/abs/math/0309471v1

Mathematics

Group Theory

Scientific paper

The local normal zeta functions of a finitely generated, torsion-free nilpotent group $G$ of class 2 depend on the geometry of the Pfaffian hypersurface associated to the bilinear form induced by taking commutators in $G$. The smallest examples of zeta functions which are not finitely uniform arise from groups whose associated Pfaffian hypersurfaces are plane curves. In this paper we study groups whose Pfaffians define singular curves, illustrating that the local normal zeta functions may indeed invoke all the degeneracy loci of the Pfaffian.

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