On linearly normal strange curves

Edoardo Ballico

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 3, page 219-222
  • ISSN: 1120-6330

Abstract

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Here we prove a numerical bound implying that, except for smooth plane conics in characteristic 2, no complete linear system maps birationally a smooth curve into a projective space with a strange curve as image.

How to cite

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Ballico, Edoardo. "On linearly normal strange curves." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.3 (1993): 219-222. <http://eudml.org/doc/244254>.

@article{Ballico1993,
abstract = {Here we prove a numerical bound implying that, except for smooth plane conics in characteristic 2, no complete linear system maps birationally a smooth curve into a projective space with a strange curve as image.},
author = {Ballico, Edoardo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Strange curve; Projective curve; Linear series; Strange point; Inseparable degree; linear series; strange point; inseparable degree; smooth strange curve},
language = {eng},
month = {9},
number = {3},
pages = {219-222},
publisher = {Accademia Nazionale dei Lincei},
title = {On linearly normal strange curves},
url = {http://eudml.org/doc/244254},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Ballico, Edoardo
TI - On linearly normal strange curves
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/9//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 3
SP - 219
EP - 222
AB - Here we prove a numerical bound implying that, except for smooth plane conics in characteristic 2, no complete linear system maps birationally a smooth curve into a projective space with a strange curve as image.
LA - eng
KW - Strange curve; Projective curve; Linear series; Strange point; Inseparable degree; linear series; strange point; inseparable degree; smooth strange curve
UR - http://eudml.org/doc/244254
ER -

References

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  2. ABRAMOVICH, D. - HARRIS, J., Abelian varieties and curves in W d ⁢ C . Compositio Math., vol. 78, 1991, 227-238. Zbl0748.14010MR1104789
  3. ARBARELLO, E. - CORNALBA, M. - GRIFFITHS, P. - HARRIS, J., Geometry of Algebraic Curves. Vol. I. Springer-Verlag, 1985. Zbl0559.14017MR770932
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  5. BALLICO, E. - HEFEZ, A., On the Galois group of a genetically etale morphism. Commun. Algebra, vol. 14, 1986, 899-909. Zbl0593.14011MR834472DOI10.1080/00927878608823344
  6. BAYER, D. - HEFEZ, A., Strange plane curves. Commun. Algebra, vol. 19, 1991, 3041-3059. Zbl0756.14018MR1132773DOI10.1080/00927879108824305
  7. CILIBERTO, C., Hilbert functions of finite sets of points and genus of a curve in a projective space. In: Space Curves. Lecture notes in Mathematics, 1266, Springer-Verlag, 1987, 24-83. Zbl0625.14016MR908707DOI10.1007/BFb0078177
  8. COPPENS, M., A remark on curves covered by coverings. Proc. Amer. Math. Soc., to appear. Zbl0807.14021MR1131033DOI10.2307/2160107
  9. EIN, L., Stable vector bundles on projective spaces in char p > 0 . Math. Ann., vol. 254, 1980, 53-72. Zbl0431.14003MR597836DOI10.1007/BF01457885
  10. EISENBUD, D. - HARMS, J., The dimension of the Chow variety of curves. Preprint. Zbl0780.14003
  11. HARRIS, J., Curve in a projective space. Les presses de L'Université de Montreal, 1982 (chapter III being joint work with D. Eisenbud). Zbl0511.14014MR685427
  12. LAKSOV, D., Indecomposability of restricted tangent bundles. In: Tableaux de Young et foncteurs de Schur en algebre et géométrie. Astérisque, 87-88, 1981, 207-219. Zbl0489.14008MR646821
  13. LLUIS, E., Variedades algebraicas con ciertas conditiones en sur tangentes. Bol. Soc. Mat. Mexicana, s. 2, vol. 7, 1962, 47-56. Zbl0119.37101
  14. RATHMANN, J., The uniform position principle for curves in characteristic p . Math. Ann., vol. 276, 1987, 565-579. Zbl0595.14041MR879536DOI10.1007/BF01456986

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