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Transactions of the American Mathematical Society

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On the Castelnuovo-Mumford regularity of connected curves


Author: Daniel Giaimo
Journal: Trans. Amer. Math. Soc. 358 (2006), 267-284
MSC (2000): Primary 13D02, 14H99
DOI: https://doi.org/10.1090/S0002-9947-05-03671-8
Published electronically: March 10, 2005
MathSciNet review: 2171233
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Abstract: In this paper we prove that the regularity of a connected curve is bounded by its degree minus its codimension plus 1. We also investigate the structure of connected curves for which this bound is optimal. In particular, we construct connected curves of arbitrarily high degree in $\mathbb{P} ^4$ having maximal regularity, but no extremal secants. We also show that any connected curve in $\mathbb{P} ^3$ of degree at least 5 with maximal regularity and no linear components has an extremal secant.


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Additional Information

Daniel Giaimo
Affiliation: Department of Mathematics, University of California–Berkeley, Berkeley, California 94720
Address at time of publication: Siebel Systems, 800 Concar Drive, San Mateo, California 94404
Email: dgiaimo@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9947-05-03671-8
Keywords: Eisenbud-Goto conjecture, Castelnuovo-Mumford regularity, connected curves
Received by editor(s): September 5, 2003
Received by editor(s) in revised form: February 15, 2004
Published electronically: March 10, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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