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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Towards a Halphen theory of
linear series on curves


Authors: L. Chiantini and C. Ciliberto
Journal: Trans. Amer. Math. Soc. 351 (1999), 2197-2212
MSC (1991): Primary 14H50
DOI: https://doi.org/10.1090/S0002-9947-99-01949-2
Published electronically: March 1, 1999
MathSciNet review: 1422598
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Abstract | References | Similar Articles | Additional Information

Abstract: A linear series $g^{N}_{\delta }$ on a curve $C\subset \mathbf{P}^{3}$ is primary when it does not contain the series cut by planes. For such series, we provide a lower bound for the degree $\delta $, in terms of deg($C$), g($C$) and of the number $s=\min \{i:h^{0}\mathcal{I}_{C}(i)\neq 0\}$. Examples show that the bound is sharp. Extensions to the case of general linear series and to the case of curves in higher projective spaces are considered.


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Additional Information

L. Chiantini
Affiliation: Università di Siena, Dipartimento di Matematica, Via del Capitano 15, 53100 Siena, Italy
Email: chiantini@unisi.it

C. Ciliberto
Affiliation: Università di Roma "Tor Vergata", Dipartimento di Matematica, Via della Ricerca Scientifica, 00133 Roma, Italy
Email: cilibert@axp.mat.uniroma2.it

DOI: https://doi.org/10.1090/S0002-9947-99-01949-2
Received by editor(s): February 22, 1996
Published electronically: March 1, 1999
Article copyright: © Copyright 1999 American Mathematical Society