Premium
Conformal Versus Topological Conjugacy of Automorphisms on Compact Riemann Surfaces
Author(s) -
Gonzálezdiez Gabino,
Hidalgo Rubén A.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002640
Subject(s) - mathematics , automorphism , topological conjugacy , riemann surface , conjugacy class , moduli space , conformal map , pure mathematics , riemann–hurwitz formula , topology (electrical circuits) , riemann sphere , algebraic number , mathematical analysis , geometric function theory , combinatorics
We produce a family of algebraic curves (closed Riemann surfaces) S λ admitting two cyclic groups H 1 and H 2 of conformal automorphisms, which are topologically (but not conformally) conjugate and such that S / H i is the Riemann sphere Ĉ. The relevance of this example is that it shows that the subvarieties of moduli space consisting of points parametrizing curves which occur as cyclic coverings (of a fixed topological type) of Ĉ need not be normal. 1991 Mathematics Subject Classification 14H10, 30F10.