NDLI: On gonality of Riemann surfaces

Content Provider	Springer Nature Link
Author	Gromadzki, Grzegorz Weaver, Anthony Wootton, Aaron
Copyright Year	2010
Abstract	A compact Riemann surface X is called a (p, n)-gonal surface if there exists a group of automorphisms C of X (called a (p, n)-gonal group) of prime order p such that the orbit space X/C has genus n. We derive some basic properties of (p, n)-gonal surfaces considered as generalizations of hyperelliptic surfaces and also examine certain properties which do not generalize. In particular, we find a condition which guarantees all (p, n)-gonal groups are conjugate in the full automorphism group of a (p, n)-gonal surface, and we find an upper bound for the size of the corresponding conjugacy class. Furthermore we give an upper bound for the number of conjugacy classes of (p, n)-gonal groups of a (p, n)-gonal surface in the general case. We finish by analyzing certain properties of quasiplatonic (p, n)-gonal surfaces. An open problem and two conjectures are formulated in the paper.
Ending Page	14
Page Count	14
Starting Page	1
File Format	PDF
ISSN	00465755
e-ISSN	15729168
Journal	Geometriae Dedicata
Issue Number	1
Volume Number	149
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-01-21
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Families, moduli, classification: algebraic theory Hyperelliptic Riemann surfaces p-Gonal Riemann surfaces Uniformization theorem Compact Riemann surfaces and uniformization Classification theory of Riemann surfaces Automorphism groups of Riemann surfaces Fuchsian groups p-Hyperelliptic Riemann surfaces Automorphisms of surfaces and higher-dimensional varieties
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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