On linear series on general $k$-gonal projective curves
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- by E. Ballico and C. Keem PDF
- Proc. Amer. Math. Soc. 124 (1996), 7-9 Request permission
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
- D. Eisenbud and J. Harris, On the Brill-Noether theorem, Algebraic geometry—open problems (Ravello, 1982) Lecture Notes in Math., vol. 997, Springer, Berlin, 1983, pp. 131–137. MR 714745, DOI 10.1007/BFb0061640
- David Eisenbud and Joe Harris, Limit linear series: basic theory, Invent. Math. 85 (1986), no. 2, 337–371. MR 846932, DOI 10.1007/BF01389094
- David Eisenbud and Joe Harris, The Kodaira dimension of the moduli space of curves of genus $\geq 23$, Invent. Math. 90 (1987), no. 2, 359–387. MR 910206, DOI 10.1007/BF01388710
- David Eisenbud and Joe Harris, When ramification points meet, Invent. Math. 87 (1987), no. 3, 485–493. MR 874033, DOI 10.1007/BF01389239
- Joe Harris and David Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), no. 1, 23–88. With an appendix by William Fulton. MR 664324, DOI 10.1007/BF01393371
- Gerald E. Welters, A theorem of Gieseker-Petri type for Prym varieties, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 4, 671–683. MR 839690, DOI 10.24033/asens.1500
Additional Information
- E. Ballico
- Affiliation: Department of Mathematics, University of Trento, 38050 Povo, Trento, Italy
- MR Author ID: 30125
- 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
- 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 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 7-9
- MSC (1991): Primary 14C95, 14C20
- DOI: https://doi.org/10.1090/S0002-9939-96-03257-1
- MathSciNet review: 1317030