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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): E. Ballico; C. Keem
Journal: Proc. Amer. Math. Soc. 124 (1996), 7-9.
MSC (1991): Primary 14C95, 14C20
MathSciNet review: 1317030
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Abstract | References | Similar articles | Additional information

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 $\dim(W^r_d(X))\leq\rho(g,r,d)+(g-2k+2):=g-(r+1) (r+g-d)+(g-2k+2)$ .

References:

EH1: D. Eisenbud and J. Harris, On the Brill-Noether theorem, Open Problems, Proceedings Ravello Conference, Lecture Notes in Math., vol. 997, Springer-Verlag, Berlin and New York, 1983, pp. 131--137. MR 85g:14031
EH2: ------, Limit linear series: Basic theory, Invent. Math. 85 (1986) 337--371.MR 87k:14024
EH3: ------, The Kodaira dimension for the moduli space of curves of genus $\geq 23$ , Invent. Math. 90 (1987), 359--387.MR 88g:14027
EH4: ------, Existence, decomposition, and limits of certain Weierstrass points, Invent. Math. 87 (1987), 495--515.MR 88a:14028b
HM: J. Harris and D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), 23--86.MR 83i:14018
W: G. Welters, A theorem of Gieseker-Petri type for Prym varieties, Ann. Sci. École Norm. Sup. (4) 18 (1985), 671--683. MR 88a:14034

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Additional Information:

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

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

DOI: 10.1090/S0002-9939-96-03257-1
PII: S 0002-9939(96)03257-1
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
Copyright of article: Copyright 1996, American Mathematical Society

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