Conformal Versus Topological Conjugacy of Automorphisms on Compact Riemann Surfaces | Zendy

Gonzálezdiez Gabino | Zendy; Hidalgo Rubén A. | Zendy

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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.

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