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On linear series
on general $k$-gonal projective curves

Authors: E. Ballico and C. Keem
Journal: Proc. Amer. Math. Soc. 124 (1996), 7-9
MSC (1991): Primary 14C95, 14C20
MathSciNet review: 1317030
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Abstract: Let $X$ be a general $k$-gonal curve of genus $g$. Here we prove a strong upper bound for the dimension of linear series on $X$, i.e. we prove that $\dim(W^r_d(X))\leq\rho(g,r,d)+(g-2k+2):=g-(r+1) (r+g-d)+(g-2k+2)$.

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Additional Information

E. Ballico
Affiliation: Department of Mathematics, University of Trento, 38050 Povo, Trento, Italy
Email: ballico@itncisca.bitnet or

C. Keem
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Email: ckeem@krsnuccl.bitnet or

Keywords: Linear series, gonality, reducible algebraic curves, limit linear series
Received by editor(s): May 18, 1994
Additional Notes: The first author was partially supported by MURST and GNSAGA of CNR (Italy). He wants to thank GARC-KOSEF (Korea) and his mathematical Korean friends both for the mathematics and the hospitality. The second author was partially supported by MOE (Korea). Both authors are indebted to GARC-KOSEF at Seoul National University, since this note owes its existence to its warm and stimulating atmosphere.
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1996 American Mathematical Society