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The irregularity of ruled surfaces in P3

  • Autores: Luis Giraldo, Ignacio Sols Lucia Árbol académico
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 2-3, 1998, págs. 325-334
  • Idioma: inglés
  • Enlaces
  • Resumen
    • Let $S$ be a ruled surface in $\textbf{P}^3$ with no multiple generators. Let $d$ and $q$ be nonnegative integers. In this paper we determine which pairs $d(d,q)$ correspond to the degree and irregularity of a ruled surface, by considering these surfaces as curves in a smooth quadric hypersurface in $\textbf{P}^5$.

  • Referencias bibliográficas
    • E. Arrondo and I. Sols, Classification of smooth congruences of low degree, J. Reine Angew. Math. 393 (1989), 199–219.
    • E. Arrondo and I. Sols, On congruences of lines in the projective space, Mém. Soc. Math. France 50, Tome 120, 1992.
    • M.A. de Cataldo, The genus of curves on the three dimensional quadric, Nagoya Math. J. 147 (1997), 193–211.
    • L. Giraldo and I. Sols, On the sectional irregularity of congruences, Manuscripta Math. 90 (1996), 239–266.
    • M. Gross, Surfaces of degree 10 in the Grassmannian of lines in 3-space, J. Reine Angew. Math. 436 (1993), 87–127.
    • L. Gruson and C. Peskine, Genre des courbes de l’espace projectif, Proceedings of Tromso conference on algebraic geometry, Springer LNM 687...
    • L. Gruson and C. Peskine, Genre des courbes de l’espace projectif (II), Ann. Sci. École Norm. Sup. 15(4) (1982), 401–418.
    • J. Harris, Curves in Projective Space, S.M.S. Presses de l’Université de Montréal, 1982.
    • R. Hartshorne, Algebraic Geometry, Springer Verlag, GTM 52, 1978.
    • R. Hernandez and I. Sols, Line congruences of low degree, Géométrie algébrique et applications II, Travaux en cours, Hermann Paris 1987, 141–154.
    • O. Panarescu, On the existence of algebraic curves in projective $n$-space, Arch. Math. 51 (1988), 255–265.
    • J. Rathmann, The genus of curves in $\mathbb{P}^4$ and $\mathbb{P}^5$, Math. Z. 202 (1989), 525–543.
    • A. Verra, Smooth surfaces of degree 9 in $G(1,3)$, Manuscripta Math. 62 (1988), 417–435.

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