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Classification of smooth congruences with a fundamental curve

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dc.book.titleProjective geometry with applications. A collection of 15 research papers
dc.contributor.authorArrondo Esteban, Enrique
dc.contributor.authorBertolini, Marina
dc.contributor.authorTurrini, Cristina
dc.contributor.editorBallico, Edoardo
dc.date.accessioned2023-06-20T21:05:35Z
dc.date.available2023-06-20T21:05:35Z
dc.date.issued1994
dc.description.abstractA 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.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/21039
dc.identifier.isbn0-8247-9278-5
dc.identifier.urihttps://hdl.handle.net/20.500.14352/60669
dc.issue.number166
dc.language.isoeng
dc.page.final56
dc.page.initial43
dc.publication.placeNew York
dc.publisherDekker
dc.relation.ispartofseriesLect. Notes Pure Appl. Math
dc.rights.accessRightsopen access
dc.subject.cdu512.772
dc.subject.keywordCongruence of lines
dc.subject.keywordGrassmannian
dc.subject.keywordfundamental curve
dc.subject.ucmÁlgebra
dc.subject.unesco1201 Álgebra
dc.titleClassification of smooth congruences with a fundamental curve
dc.typebook part
dcterms.referencesAlzati, A., 3-Scroll immersi in G(1, 4), Ann. Univ. Ferrara, 32 (1986), 45-54. Arbarello, E.– Cornalba, M.– Griffiths, P.– Harris, J., Geometry of Algebraic Curves, Vol. I Grund. der Math. Wissen. 267 Springer-Verlag (1985). Arrondo, E.– Gross, M., On smooth surfaces in Gr(1,P3) with a fundamental curve, to appear in Man. Math. Ein, L., Non-degenerate surfaces of degree n + 3 in Pn, Crelle Journal Reine Angew. Math. 351 (1984), 1-11. Fano, G., Sulle congruenze di rette del terzo ordine prive di linea singolare, Att. Acc. di Scienze Torino 29 (1984), 474-493. Fano, G., Nuove ricerche sulle congruenze di rette del 30 ordine prive di linea singolare, Memoria della Reale Acad. Sc. Torino (2) 51 (1902), 1-79. Fulton, W., Intersection Theory, Ergebnisse (3) 2, Springer (1984). Goldstein, N. Scroll surfaces in Gr(1,P3), Conference on Algebraic Varieties of small dimension (Turin 1985), Rend. Sem. Mat. Univ. Politecnica, Special Issue (1987) 69-75. Gross, M., Surfaces in the four-dimensional Grassmannian, Ph. D. thesis, Berkeley (1990). Gross, M., The distribution of bidegrees of smooth surfaces in Gr(1,P3), Math. Ann. 292 (1992), 127-147. Roth, L., On the projective classification of surfaces, Proc. London Math. Soc., 42 (1937), 142-170.
dspace.entity.typePublication
relation.isAuthorOfPublication5bd88a9c-e3d0-434a-a675-3221b2fde0e4
relation.isAuthorOfPublication.latestForDiscovery5bd88a9c-e3d0-434a-a675-3221b2fde0e4

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