Título: | The universal rank-(n ? 1) bundle on G(1, n) restricted to subvarieties |
Autores: | Arrondo Esteban, Enrique |
Tipo de documento: | texto impreso |
Editorial: | Springer, 1998 |
Dimensiones: | application/pdf |
Nota general: |
info:eu-repo/semantics/openAccess info:eu-repo/semantics/restrictedAccess |
Idiomas: | , |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría , Tipo = Artículo |
Resumen: |
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. |
En línea: | https://eprints.ucm.es/id/eprint/21007/1/arrondo_the_universal.pdf |
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