Mallavibarrena Martínez de Castro, Raquel and Lanteri, Antonio (2009) Osculating properties of decomposable scrolls. Mathematische Nachrichten, 282 (11). pp. 1548-1566. ISSN 0025-584X
Restricted to Repository staff only until 31 December 2020.
Osculating 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.
|Uncontrolled Keywords:||scroll (non-normal); osculating space; inflectional locus; (higher) discriminant locus|
|Subjects:||Sciences > Physics > Astrophysics|
E. 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).
|Deposited On:||03 Oct 2012 08:06|
|Last Modified:||07 Feb 2014 09:32|
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