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A vanishing theorem for reducible space curves and the construction of smooth space curves in the Range C

Edoardo Ballico
대한수학회 (The Korean Mathematical Society)|2019.01|대한수학회논문집 (Communications of the KMS)|제34권 제1호|pp. 105-111|DOI 10.4134/CKMS.c180046

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참고문헌

키워드

linkageHilbert functionspace curveHalphen's gapsHart\-shorne-Rao module
주제분류수학

초록

Let $Y\subset \PP^3$ be a degree $d$ reduced curve with only planar singularities. We prove that $h^i(\Ii _Y(t)) =0$, $i=1,2$, for all $t\ge d-2$. 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 $g$, $h^0(\Ii _C(s)) =1$ and describe the Hartshorne-Rao module of $C$.

Abstract

Let $Y\subset \PP^3$ be a degree $d$ reduced curve with only planar singularities. We prove that $h^i(\Ii _Y(t)) =0$, $i=1,2$, for all $t\ge d-2$. 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 $g$, $h^0(\Ii _C(s)) =1$ and describe the Hartshorne-Rao module of $C$.

참고문헌 (17)

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