Bujalance, E. and Etayo Gordejuela, J. Javier and Gamboa Mutuberria, Jose Manuel and Gromadzki, G. (2011) The Gonality Of Riemann Surfaces Under Projections By Normal Coverings. Journal Of Pure And Applied Algebra, 215 (5). pp. 983-988. ISSN 0022-4049
![[img]](/style/images/fileicons/application_pdf.png) | PDF Restricted to Repository staff only until 2020. 240Kb |
Official URL: http://www.sciencedirect.com/science/article/pii/S0022404910001581
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].
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Mathematics, Applied; Mathematics |
| Subjects: | Sciences > Mathematics > Functions |
| ID Code: | 15207 |
| References: | 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). |
| Deposited On: | 16 May 2012 10:24 |
| Last Modified: | 30 Nov 2012 10:06 |
Repository Staff Only: item control page
