Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A VANISHING THEOREM FOR REDUCIBLE SPACE CURVES AND THE CONSTRUCTION OF SMOOTH SPACE CURVES IN THE RANGE C

  • Received : 2018.02.03
  • Accepted : 2018.05.24
  • Published : 2019.01.31
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Abstract

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.

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References

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