On the rationality of the variety of smooth rational space curves with fixed degree and normal bundle
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- by Edoardo Ballico PDF
- Proc. Amer. Math. Soc. 91 (1984), 510-512 Request permission
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 $a > 0$.References
- D. Eisenbud and A. Van de Ven, On the normal bundles of smooth rational space curves, Math. Ann. 256 (1981), no. 4, 453–463. MR 628227, DOI 10.1007/BF01450541
- David Eisenbud and A. Van de Ven, On the variety of smooth rational space curves with given degree and normal bundle, Invent. Math. 67 (1982), no. 1, 89–100. MR 664325, DOI 10.1007/BF01393373 A. Hirschowitz and M. S. Narasimhan, Fibres de’t Hooft et application, Enumerative Geometry and Classical Algebraic Geometry, Progress in Math., vol. 24. Birkhäuser, Basel, 1982. J. Kollar and F. O. Schreyer, The moduli of curves is stably rational for $g \leqslant 6$ (preprint).
- P. E. Newstead, Comparison theorems for conic bundles, Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 1, 21–31. MR 611282, DOI 10.1017/S0305004100058497 J. P. Serre, Espaces fibres algébriques, Séminaire C. Chevalley 1958 Anneaux de Chow et Applications, Exp. 1, Secrétariat mathématique, Paris, 1958.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 510-512
- MSC: Primary 14H10; Secondary 14N05
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746078-8
- MathSciNet review: 746078