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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The restricted tangent bundle of a rational curve on a quadric in $ {\bf P}\sp 3$


Author: Maria-Grazia Ascenzi
Journal: Proc. Amer. Math. Soc. 98 (1986), 561-566
MSC: Primary 14H45; Secondary 14H50
DOI: https://doi.org/10.1090/S0002-9939-1986-0861750-9
MathSciNet review: 861750
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Abstract: Let $ {\psi ^*}{T_{{{\mathbf{P}}^3}}}$ be the pull-back of the tangent bundle to $ {{\mathbf{P}}^3}$ via a parametrization $ \psi $ of a rational, reduced, irreducible curve $ C$ in $ {{\mathbf{P}}^3}$ contained in an irreducible quadric surface. Since $ C$ is rational, the bundle $ {\psi ^*}{T_{{{\mathbf{P}}^3}}}$ splits into the direct sum of three line bundles.

In this paper we study the relationship between the degrees of the line bundles of the splitting of $ {\psi ^*}{T_{{{\mathbf{P}}^3}}}$ and the geometry of the curve $ C$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0861750-9
Article copyright: © Copyright 1986 American Mathematical Society