Arrondo Esteban, Enrique2023-06-202023-06-201998E. 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, 19930010-0757https://hdl.handle.net/20.500.14352/58419The 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.engjournal articleopen access514.144Grassmannianslinear normalityprojectionsdualityGeometría1204 Geometría