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On curves on rational surface scrolls

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Abstract

For a smooth curve C in \({{\mathbb {P}}}^{r_0}\) lying on a rational surface scroll, we try to identify those complete and base point free linear series of small degree which are not obtainable just by projection from C.

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References

  1. Arbarello, E., Cornalba, M., Griffiths, P.A., Harris, J.: Geometry of Algebraic Curves. I. Springer, Berlin (1985)

    Book  MATH  Google Scholar 

  2. Coppens, M., Keem, C., Martens, G.: Primitive linear series on curves. Manuscripta Math. 77, 237–264 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ciliberto, C., Lazarsfeld, R.: On the uniqueness of certain linear series on some classes of curves. Lect. Notes Math. 1092, 198–213 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics, vol. 52. Springer, Berlin (1977)

    Book  Google Scholar 

  5. Lange, H., Martens, G.: On the gonality sequence of an algebraic curve. Manuscripta Math. 137, 457–473 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Martens, G.: The gonality of curves on a Hirzebruch surface. Arch. Math. 67, 349–352 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Reider, I.: Some applications of Bogomolov’s theorem. In: Catanese, F. (ed.) Problems in the Theory of Surfaces and their Classification, Symposia Mathematica, vol. 32, pp. 376–410. Academic Press, Cambridge (1991)

    Google Scholar 

  8. Schreyer, F.-O.: Syzygies of curves with special pencils. Brandeis Univ., Thesis (1983)

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Correspondence to Gerriet Martens.

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Martens, G. On curves on rational surface scrolls. Arch. Math. 112, 489–495 (2019). https://doi.org/10.1007/s00013-018-1276-8

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  • DOI: https://doi.org/10.1007/s00013-018-1276-8

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