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- Title
Non-degenerate curves with maximal Hartshorne-Rao module.
- Authors
Uwe Nagel
- Abstract
Extending results for space curves we establish bounds for the cohomology of a non-degenerate curve in projective $n$-space. As a consequence, for any given $n$ we determine all possible pairs $(d, g)$ where $d$ is the degree and $g$ is the (arithmetic) genus of the curve. Furthermore, we show that curves attaining our bounds always exist and describe properties of these extremal curves. In particular, we determine the Hartshorne-Rao module, the generic initial ideal and the graded Betti numbers of an extremal curve.
- Subjects
CURVES; PROJECTIVE spaces; MATHEMATICS
- Publication
Mathematische Zeitschrift, 2003, Vol 244, Issue 4, p753
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-003-0520-4