## On the Castelnuovo-Mumford regularity of connected curves

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- by Daniel Giaimo PDF
- Trans. Amer. Math. Soc.
**358**(2006), 267-284 Request permission

## 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.## References

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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
- Received by editor(s): September 5, 2003
- Received by editor(s) in revised form: February 15, 2004
- Published electronically: March 10, 2005
- © Copyright 2005 American Mathematical Society
- 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
- MathSciNet review: 2171233