Classification of smooth congruences with a fundamental curve
A congruence of lines is a (n−1)-dimensional family of lines in Pn (over C), i.e. a variety Y of dimension (and hence of codimension) n − 1 in the Grassmannian Gr(1, Pn). A fundamental curve for Y is a curve C Pn which meets all the lines of Y . In this paper the authors classify all smooth congruen...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 1994 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/60669 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/60669 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.772 Congruence of lines Grassmannian fundamental curve Álgebra 1201 Álgebra |
| Sumario: | A congruence of lines is a (n−1)-dimensional family of lines in Pn (over C), i.e. a variety Y of dimension (and hence of codimension) n − 1 in the Grassmannian Gr(1, Pn). A fundamental curve for Y is a curve C Pn which meets all the lines of Y . In this paper the authors classify all smooth congruences with fundamental curve C generalizing a paper by E. Arrondo and M. Gross [Manuscr. 79, No. 3-4, 283-298 (1993; Zbl 0803.14019)], where the case n = 3 was treated. An explicit construction for all possible congruences that they found is also given. |
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