On the Castelnuovo-Mumford regularity of connected curves

Giaimo, Daniel

doi:10.1090/S0002-9947-05-03671-8

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.

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