• Title/Summary/Keyword: Hartshorne-Rao module

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A VANISHING THEOREM FOR REDUCIBLE SPACE CURVES AND THE CONSTRUCTION OF SMOOTH SPACE CURVES IN THE RANGE C

  • Ballico, Edoardo
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.105-111
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    • 2019
  • Let $Y{\subset}{\mathbb{P}}^3$ be a degree d reduced curve with only planar singularities. We prove that $h^i({\mathcal{I}}_Y(t))=0$, i = 1, 2, for all $t{\geq}d-2$. We use this result and linkage to construct some triples (d, g, s), $d>s^2$, with very large g for which there is a smooth and connected curve of degree d and genus g, $h^0({\mathcal{I}}_C(s))=1$ and describe the Hartshorne-Rao module of C.