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

Published electronically:
March 10, 2005

MathSciNet review:
2171233

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Abstract | References | Similar Articles | Additional Information

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 having maximal regularity, but no extremal secants. We also show that any connected curve in 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:
http://dx.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