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Bounding families of ruled surfaces

Gallego Rodrigo, Francisco Javier and Giraldo Suárez, Luis and Sols Lucía, Ignacio (1996) Bounding families of ruled surfaces. Proceedings of the American Mathematical Society, 124 (10). pp. 2943-2951. ISSN 1088-6826

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Abstract

In this paper we provide a sharp bound for the dimension of a family of ruled surfaces of degree d in P3 K. We also _nd the families with maximal dimension: the family of ruled surfaces containing two unisecant skew lines, when d _ 9 and the family of rational ruled surfaces, when d _ 9.
The first tool we use is a Castelnuovo-type bound for the irregularity of ruled surfaces in Pn K. The second tool is an exact sequence involving the normal sheaf of a curve in the grassmannian. This sequence is analogous to the one constructed by Eisenbud and Harris in 1992, where they deal with the problem
of bounding families of curves in projective space. However, our construction is more general since we obtain the mentioned sequence by purely algebraic means, studying the geometry of ruled surfaces and of the grassmannian.

Item Type:Article
Additional Information:First published in Proceedings of the American Mathematical Society in Volume 124, Number 10, October 1996, published by the American Mathematical
Uncontrolled Keywords:Castelnuovo bound, Dimension of a family of ruled surfaces, Irregularity, Ruled surfaces, Curve in the grassmannian
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:12601
Deposited On:25 Apr 2011 21:07
Last Modified:06 Feb 2014 09:28

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