RT Journal Article
T1 The Gonality Of Riemann Surfaces Under Projections By Normal Coverings
A1 Bujalance, E.
A1 Etayo Gordejuela, J. Javier
A1 Gamboa Mutuberria, José Manuel
A1 Gromadzki, G.
AB 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 thegonalities 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].
PB Elsevier Science
SN 0022-4049
YR 2011
FD 2011
LK https://hdl.handle.net/20.500.14352/42173
UL https://hdl.handle.net/20.500.14352/42173
LA eng
NO 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).
NO Proyecto Santander Complutense[PR34/07-15813]; GAAR Grupos UCM[910444]; Polish Ministry of Sciences and Higher Education[NN201366436]; [MTM2008-00250]; [MTM2008-00272]
DS Docta Complutense
RD 8 may 2024