On the Castelnuovo-Mumford regularity of connected curves

Details On the Castelnuovo-Mumford regularity of connected curves On the Castelnuovo-Mumford regularity of connected curves

2003-09-02

arxiv.org/abs/math/0309051v1

Mathematics

Algebraic Geometry

21 pages, 2 figures

Scientific paper

In this paper we prove the Eisenbud-Goto conjecture for connected curves. 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 projective 4-space having maximal regularity, but no extremal secants. We also show that any connected curve in projective 3-space of degree at least 5 that has no linear components and has maximal regularity has an extremal secant.

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