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The universal rank-(n − 1) bundle on G(1, n) restricted to subvarieties

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Arrondo Esteban, Enrique (1998) The universal rank-(n − 1) bundle on G(1, n) restricted to subvarieties. Collectanea mathematica, 49 (2-3). pp. 173-183. ISSN 0010-0757

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Official URL: http://dmle.cindoc.csic.es/pdf/COLLECTANEAMATHEMATICA_1998_49_02_03.pdf




Abstract

The author has, in several articles, studied varieties in the Grassmannian G(k, n) of kplanes in projective n-space, that are projections from a variety in G(k,N). In the case
k = 1 the varieties of dimension n−1 in G(1, n) that are projections from G(1,N) were studied by E. Arrondo and I. Sols [“On congruences of lines in the projective space”,
M´em. Soc. Math. Fr., Nouv. S´er. 50 (1992; Zbl 0804.14016)] and solved for n = 3 by E. Arrondo [J. Algebr. Geom. 8, No. 1, 85-101 (1999; Zbl 0945.14030)]. In the paper
under review the author studies the other extreme k = n−1, n−2. The case k = n−1 is solved completely, and in the case k = n−2 it is shown that if Y is a smooth variety of dimension s in G(1, n) whose dual Y in G(n − 2, n) is a non-trivial projection from G(n − 2, n + 1), then s = n − 1 and Y is completely classified. The methods are from
classical projective geometry and based upon results by E. Rogora [Manuscr. Math. 82, No. 2, 207-226 (1994; Zbl 0812.14038)] and B. Segre.


Item Type:Article
Uncontrolled Keywords:Grassmannians; linear normality; projections; duality
Subjects:Sciences > Mathematics > Geometry
ID Code:21007
Deposited On:23 Apr 2013 14:16
Last Modified:03 Oct 2018 11:43

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