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Osculating properties of decomposable scrolls

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dc.contributor.authorMallavibarrena Martínez de Castro, Raquel
dc.contributor.authorLanteri, Antonio
dc.date.accessioned2023-06-20T00:17:22Z
dc.date.available2023-06-20T00:17:22Z
dc.date.issued2009-11
dc.description.abstractOsculating spaces of decomposable scrolls (of my genus and not necessarily normal) arc studied and their inflectional loci are related to those of their generating curves by using systematically an idea introduced by Piene and Sacchiero in the setting of rational normal scrolls. In this broader setting the extra components of the second discriminant locus-deriving from flexes-are investigated and a new class of uninflected surface scrolls is presented and characterized. Further properties related to osculation are discussed for (not necessarily decomposable) scrolls.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipItalian Government
dc.description.sponsorshipSpanish Ministry of Education
dc.description.sponsorshipUniversity of Milan
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16603
dc.identifier.doi10.1002/mana.200610834
dc.identifier.issn0025-584X
dc.identifier.officialurlhttp://onlinelibrary.wiley.com/doi/10.1002/mana.200610834/pdf
dc.identifier.urihttps://hdl.handle.net/20.500.14352/42336
dc.issue.number11
dc.journal.titleMathematische Nachrichten
dc.language.isoeng
dc.page.final1566
dc.page.initial1548
dc.publisherWiley-Blackwell
dc.relation.projectIDBFM2003-03917/MATE
dc.relation.projectIDSantander/UCM PR27/05-13876
dc.rights.accessRightsrestricted access
dc.subject.cdu521.1
dc.subject.keywordscroll (non-normal)
dc.subject.keywordosculating space
dc.subject.keywordinflectional locus
dc.subject.keyword(higher) discriminant locus
dc.subject.ucmAstrofísica
dc.titleOsculating properties of decomposable scrolls
dc.typejournal article
dc.volume.number282
dcterms.referencesE. Arbarello, M. Cornalba, Ph. Griffiths, and J. Harris, Geometry of Algebraic Curves, Vol. I (Springer, New York, 1985). E. Ballico and C. Fontanari, On the osculatory behaviour of higher dimensional projective varieties, Collect. Math. 55, 229–236 (2004). E. Ballico, R. Piene, and H. Tai, A characterization of balanced rational normal surface scrolls in terms of their osculating spaces, II, Math. Scand. 70, 204–206 (1992). R. Hartshorne, Algebraic Geometry (Springer, New York, 1977). T. Johnsen, Plane projections of a smooth space curve, in: Parameter Spaces, Banach Center Publications Vol. 36(Polish Acad. Sci., Warsaw, 1996), pp. 89–110. A. Lanteri, On the osculatory behavior of surface scrolls, Le Matematiche (Catania) 55, 447–458 (2000). R. Mallavibarrena and R. Piene, Duality for elliptic normal surface scrolls, in: Enumerative Algebraic Geometry, edited by S. L. Kleiman and A. Thorup, Contemporary Mathematics Vol. 123 (Amer. Math. Soc., Providence, RI, 1991), pp. 149–160. R. Piene, Numerical characters of a curve in projective n -space, in: Real and Complex Singularities, edited by P. Holm (Sijthoff and Noordhoff, Groningen, 1978), pp. 475–496. R. Piene and G. Sacchiero, Duality for rational normal scrolls, Comm. Algebra 12, 1041–1066 (1984). R. Piene and H. S. Tai, A characterization of balanced rational normal scrolls in terms of their osculating spaces, in: Proceedings of the International Conference on Enumerative Geometry, Sitges 1987, edited by S. Xambo–Descamps, Lecture Notes in Mathematics Vol. 1436 (Springer-Verlag, New York–Heidelberg–Berlin, 1990), pp. 215–224. T. Shifrin, The osculatory behavior of surfaces in P 5 , Pacif. J. Math. 123, 227–256 (1986).
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