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On the connectedness of the scheme of multisecants to a projective curve

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Abstract

Here we study the connectedness of the scheme of multisecant linear spaces to a curveC ⊂P n. In particular we prove the connectedness of the scheme of trisecant lines of a smoothC ⊂P 3 with non-special hyperplane section.

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References

  1. Arbarello, E., Cornalba, M., Griffiths, P. and Harris, J.:Geometry of Algebraic Curves, Vol. I. Grundlehren Math. Wiss. 267, Springer-Verlag, Berlin, Heidelberg, New York, 1985.

    Google Scholar 

  2. Ballico, E., and Ellia, Ph.: Beyond the maximal rank conjecture for curves inP 3, inSpace Curves, Lect. Notes in Math. 1266, Springer Verlag, Berlin, Heidelberg, New York, 1987, pp. 1–23.

    Google Scholar 

  3. Ballico, E. and Ellia, Ph.: On the existence of curves with maximal rank inP n,J. reine angew. Math. 397 (1989), 1–22.

    Google Scholar 

  4. Coppens, M. and Martens, G.: Secant spaces and Clifford's theorem,Compositio Math. 78 (1991), 193–212.

    Google Scholar 

  5. Ein, L.: Hilbert scheme of smooth space curves,Ann. Scient. Ec. Norm. Sup. (4) 19 (1986), 469–478.

    Google Scholar 

  6. Eisenbud, D. and Harris, J.: Divisors on general curves and cuspidal rational curves,Invent. Math. 74 (1983), 371–418.

    Google Scholar 

  7. Fulton, W. and Lazarsfeld, R.: On the connectedness of degeneracy loci and special divisors,Acta Math. 146 (1981), 271–283.

    Google Scholar 

  8. Gruson, L. and Peskine, C.: Courbe de l'espace projectif, variétés des sécantes, inEnumerative Geometry and Classical Algebraic Geometry, Progress in Math. 24, Birkhäuser, Basel, 1982, pp. 1–31.

    Google Scholar 

  9. Johsen, T.: Local properties of secant varieties in symmetric products, Part II,Trans. Amer. Math. Soc. 313 (1989), 205–220.

    Google Scholar 

  10. Laytimi, F.: Courbe des trisécantes à une courbe elliptique lisse deP 3,Arch. Math. 57 (1991), 617–621.

    Google Scholar 

  11. Laytimi, F.: Courbe des trisecantes a une courbe lisse deP 3 de degreed>2g+1,Math. Ann. 294 (1992), 459–462.

    Google Scholar 

  12. Mattuck, A.: Secant bundles on symmetric products,Amer. J. Math. 87 (1965), 779–797.

    Google Scholar 

  13. Shiffman, B. and Sommese, J. A.:Vanishing Theorems on Complex Manifolds, Progress in Math. 56, Birkhäuser, Basel, 1985.

    Google Scholar 

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  1. Dept. of Mathematics, Università di Trento, 38050, Povo (TN), Italy

    E. Ballico

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  1. E. Ballico
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Ballico, E. On the connectedness of the scheme of multisecants to a projective curve. Geom Dedicata 53, 327–332 (1994). https://doi.org/10.1007/BF01264005

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