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...

ver descrição completa

Detalhes bibliográficos
Autores: Arrondo Esteban, Enrique, Bertolini, Marina, Turrini, Cristina
Tipo de documento: capítulo de livro
Data de publicação:1994
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/60669
Acesso em linha:https://hdl.handle.net/20.500.14352/60669
Access Level:Acceso aberto
Palavra-chave:512.772
Congruence of lines
Grassmannian
fundamental curve
Álgebra
1201 Álgebra
Descrição
Resumo: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.