Publication: The universal rank-(n − 1) bundle on G(1, n) restricted to subvarieties
Loading...
Official URL
Full text at PDC
Publication Date
1998
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
PPU
Citations
Exportar
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.
Description
UCM subjects
Unesco subjects
Keywords
Citation
E. Arrondo, Projections of Grassmannians of lines and characterization of Veronese varieties, preprint (1997).
E. Arrondo, M. Bertolini and C. Turrini, Classification of smooth congruences with a fundamental curve, pages 43-56 in Projective geometry with applications (ed. E. Ballico), Marcel Dekker, New York, 1994.
E. Arrondo and I. Sols, On congruences of lines in the projective space, Soc. Math. France (M´em. 50), 1992.
E. Rogora, Varieties with many lines, Manuscripta Math. 82 (1994),207-226.
B. Segre, Sulle Vn aventi pi`u di ∞n−k Sk, I and II, Rend. dell’Acad. Naz. Lincei, vol. V (1948), 193-157 and 217-273.
F. Severi, Intorno ai punti doppi impropri di una superficie generale dello spazio a quattro dimensioni, e a suoi punti tripli apparenti Rend. Circ. Mat. Palermo II, 15 (1901), 377–401.
F.L Zak, Tangents and Secants of Algebraic Varieties, Transl. Math. Monographs AMS, vol. 127, Providence, RI, 1993