RT Journal Article
T1 The universal rank-(n − 1) bundle on G(1, n) restricted to subvarieties
A1 Arrondo Esteban, Enrique
AB 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.
PB PPU
SN 0010-0757
YR 1998
FD 1998
LK https://hdl.handle.net/20.500.14352/58419
UL https://hdl.handle.net/20.500.14352/58419
LA eng
NO 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
NO DGICYT
DS Docta Complutense
RD 5 may 2024