On the Castelnuovo-Mumford regularity of connected curves

Daniel Giaimo

On the Castelnuovo-Mumford regularity of connected curves

Algebraic Geometry 2007-05-23 v1 Commutative Algebra

Authors: Daniel Giaimo

Abstract

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.

Keywords

Castelnuovo-Mumford regularity connected curve Eisenbud-Goto conjecture extremal secant projective space

Cite

@article{arxiv.math/0309051,
  title  = {On the Castelnuovo-Mumford regularity of connected curves},
  author = {Daniel Giaimo},
  journal= {arXiv preprint arXiv:math/0309051},
  year   = {2007}
}

Comments

21 pages, 2 figures

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