TY - JOUR
T1 - Non-degenerate curves with maximal Hartshorne-Rao module
AU - Nagel, Uwe
PY - 2003/8
Y1 - 2003/8
N2 - 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.
AB - 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.
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U2 - 10.1007/s00209-003-0520-4
DO - 10.1007/s00209-003-0520-4
M3 - Article
AN - SCOPUS:0042918135
SN - 0025-5874
VL - 244
SP - 753
EP - 773
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 4
ER -