Publication: The Gonality Of Riemann Surfaces Under Projections By Normal Coverings
Loading...
Files
Full text at PDC
Publication Date
2011
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science
Citations
Exportar
Abstract
A compact Riemann surface X of genus g ≥ 2 which can be realized as a q-fold, normal covering of a compact Riemann surface of genus p is said to be (q, p)-gonal.
In particular the notion of (2, p)-gonality coincides with p-hyperellipticity and (q, 0)-gonality coincides with ordinary q-gonality.
Here we completely determine the relationship between the
gonalities of X and Y for an N-fold normal covering X → Y between compact Riemann surfaces X and Y.
As a consequence we obtain classical results due to Maclachlan (1971) [5] and Martens (1977) [6].
Description
UCM subjects
Unesco subjects
Keywords
Citation
E. Bujalance, J.J. Etayo, J.M. Gamboa, G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces, A Combinatorial Approach, in: Lecture Notes in Math., vol. 1439, Springer Verlag, 1990.
G. Castelnuovo, Ricerche de geometria sulle curve algebriche, Atti Acad. Sci. Torino 24 (1889) 346–373. (Memorie Scelte, Zanichelli Bologna, 1937, pp. 19–44).
H.M. Farkas, I. Kra, Riemann Surfaces, in: Graduate Text in Mathematics, Springer-Verlag, 1980.
G. Gromadzki, A. Weaver, A. Wootton, On gonality of Riemann surfaces. Geom. Dedicata (in press).
C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. J. Math. Oxford 22 (2) (1971) 117–123.
H.H. Martens, A remark on Abel’s Theorem and the mapping of linear series, Comment. Math. Helv. 52 (1977) 557–559.
F. Severi, Vorlesungen über algebraische Geometrie, Teubner, Leipzig (1921).