Proceedings of the American Mathematical Society

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

 

 

On the rationality of the variety of smooth rational space curves with fixed degree and normal bundle


Author: Edoardo Ballico
Journal: Proc. Amer. Math. Soc. 91 (1984), 510-512
MSC: Primary 14H10; Secondary 14N05
MathSciNet review: 746078
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Abstract: Let $ {\tilde S_{n,a}}$ be the variety of smooth, rational curves of degree $ n$ in $ {{\mathbf{P}}_3}$ whose normal bundle has a factor of degree $ 2n - 1 + a$ and a factor of degree $ 2n - 1 - a$. In this paper we prove that $ {\tilde S_{n,a}}$ is rational if $ n - a$ is even and $ a > 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746078-8
Keywords: Rational curve, projective space, rational variety, normal bundle, degree, irreducible variety, principal bundle, projective group
Article copyright: © Copyright 1984 American Mathematical Society