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A Vanishing Theorem for the Twisted Normal Bundle of Curves in $\mathbb{P}^{n}$, $n\geqslant 8$

Part of: Curves

Published online by Cambridge University Press:  30 August 2019

E. Ballico
E. Ballico*
Affiliation:
Department of Mathematics, University of Trento, 38123Povo (TN), Italy Email: ballico@science.unitn.it
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Abstract

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We prove the existence of a smooth and non-degenerate curve $X\subset \mathbb{P}^{n}$, $n\geqslant 8$, with $\deg (X)=d$, $p_{a}(X)=g$, $h^{1}(N_{X}(-1))=0$, and general moduli for all $(d,g,n)$ such that $d\geqslant (n-3)\lceil g/2\rceil +n+3$. It was proved by C. Walter that, for $n\geqslant 4$, the inequality $2d\geqslant (n-3)g+4$ is a necessary condition for the existence of a curve with $h^{1}(N_{X}(-1))=0$.

Keywords

projective curvenormal bundletwisted normal bundle

MSC classification

Primary: 14H50: Plane and space curves
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 1 , March 2020 , pp. 1 - 5
Copyright
© Canadian Mathematical Society 2019

Footnotes

The author was partially supported by MIUR and GNSAGA of INdAM (Italy).

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