[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2011.48.5.1015

ON FIXED POINTS ON COMPACT RIEMANN SURFACES

Gromadzki, Grzegorz (Institute of Mathematics University of Gdansk)

Publication Information

Bulletin of the Korean Mathematical Society / v.48, no.5, 2011 , pp. 1015-1021 More about this Journal

Abstract

A point of a Riemann surface X is said to be its fixed point if it is a fixed point of one of its nontrivial holomorphic automorphisms. We start this note by proving that the set Fix(X) of fixed points of Riemann surface X of genus g ${\geq}$ 2 has at most 82(g-1) elements and this bound is attained just for X having a Hurwitz group of automorphisms, i.e., a group of order 84(g-1). The set of such points is invariant under the group of holomorphic automorphisms of X and we study the corresponding symmetric representation. We show that its algebraic type is an essential invariant of the topological type of the holomorphic action and we study its kernel, to find in particular some sufficient condition for its faithfulness.

Keywords

automorphisms of Riemann surfaces; fixed point; Fuchsia groups; symmetric representation;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

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