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Double covering of curves |
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| Authors: | Edoardo Ballico Changho Keem Seungsuk Park |
| Affiliation: | Department of Mathematics, Università di Trento, 38050 Povo(TN), Italy ; Department of Mathematics, Seoul National University, Seoul 151-742, South Korea ; Department of Mathematics, Seoul National University, Seoul 151-742, South Korea |
| Abstract: | Let  be a smooth projective algebraic curve of genus  and  an integer with  . For all integers  we prove the existence of a double covering  with  a smooth curve of genus  and the existence of a degree  morphism  that does not factor through  . By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound  ). |
| Keywords: | Double coverings base-point-free pencil Castelnuovo-Severi inequality Brill-Noether theory |
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