Nilpotent groups of automorphisms of families of Riemann surfaces

Abstract

In this article we extend results of Zomorrodian to determine upper bounds for the order of a nilpotent group of automorphisms of a complex $d$-dimensional family of compact Riemann surfaces, where $d⩾1.$ We provide conditions under which these bounds are sharp. In addition, for the one-dimensional case we construct and describe an explicit family attaining the bound for infinitely many genera. We obtain similar results for the case of $p$-groups of automorphisms.

arXiv comment19 pages, To appear in Annali di Matematica Pura ed Applicata

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