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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
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$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1986 American Mathematical Society

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