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RISS 인기검색어
- 검색키워드
- 저자 : Grzegorz Gromadzki (검색결과 2 건)
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ON FIXED POINTS ON COMPACT RIEMANN SURFACES
Gromadzki, Grzegorz Korean Mathematical Society 2011 대한수학회보 Vol.48 No.5
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.
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On fixed points on compact Riemann surfaces
Grzegorz Gromadzki 대한수학회 2011 대한수학회보 Vol.48 No.5
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 a Riemann surface X of genus g≥ 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 conditions for its faithfulness.
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