Line Congruences of Low Order

A line congruence is an irreducible subvariety of dimension n−1 in the Grassmannian of lines in Pn. There are two numerical invariants associated to a line congruence: the order, which is the number of lines passing through a general point of Pn, and the class, which is the number of lines of the co...

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Detalles Bibliográficos
Autor: Arrondo Esteban, Enrique
Tipo de recurso: artículo
Fecha de publicación:2002
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/57036
Acceso en línea:https://hdl.handle.net/20.500.14352/57036
Access Level:acceso abierto
Palabra clave:512
Grassmannians
Schubert varieties
Álgebra
1201 Álgebra
Descripción
Sumario:A line congruence is an irreducible subvariety of dimension n−1 in the Grassmannian of lines in Pn. There are two numerical invariants associated to a line congruence: the order, which is the number of lines passing through a general point of Pn, and the class, which is the number of lines of the congruence contained in a general hyperplaneH and meeting a general line inH. The paper reviews the classification of line congruences of order 0 and 1, and then gives some new results online congruences of order 2 in P3, which is a work in progress. The last section states some open questions.