Minimality of subcanonical curves

Mireille Martin-Deschamps[1]

  • [1] Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques, Bâtiment Fermat, 45 avenue des États-Unis, 78035 Versailles Cedex (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 4, page 1027-1040
  • ISSN: 0373-0956

Abstract

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We prove the following result: let ℰ be a rank 2 bundle on the projective space ℙ 3 of dimension 3, and n an integer such that H 0 ℰ ( n - 1 ) = 0 and H 0 ℰ ( n ) ≠ 0 . Let C be a curve which is the zero locus of a section of ℰ ( n ) . Then C is minimal in its biliaison class.

How to cite

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Martin-Deschamps, Mireille. "Minimalité des courbes sous-canoniques." Annales de l’institut Fourier 52.4 (2002): 1027-1040. <http://eudml.org/doc/116001>.

@article{Martin2002,
abstract = {Soient $\{\mathcal \{E\}\}$ un fibré de rang 2 sur l’espace projectif de dimension 3 sur un corps algébriquement clos et $n$ un entier tel que $H^0\{\mathcal \{E\}\}(n-1)=0$ et $H^0\{\mathcal \{E\}\}(n)\ne 0$. Toute courbe $C$ schéma des zéros d’une section non nulle de $\{\mathcal \{E\}\}(n)$ est une courbe minimale dans sa classe de biliaison.},
affiliation = {Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques, Bâtiment Fermat, 45 avenue des États-Unis, 78035 Versailles Cedex (France)},
author = {Martin-Deschamps, Mireille},
journal = {Annales de l’institut Fourier},
keywords = {fiber bundle; biliaison; minimal curve; subcanonical curve},
language = {fre},
number = {4},
pages = {1027-1040},
publisher = {Association des Annales de l'Institut Fourier},
title = {Minimalité des courbes sous-canoniques},
url = {http://eudml.org/doc/116001},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Martin-Deschamps, Mireille
TI - Minimalité des courbes sous-canoniques
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 4
SP - 1027
EP - 1040
AB - Soient ${\mathcal {E}}$ un fibré de rang 2 sur l’espace projectif de dimension 3 sur un corps algébriquement clos et $n$ un entier tel que $H^0{\mathcal {E}}(n-1)=0$ et $H^0{\mathcal {E}}(n)\ne 0$. Toute courbe $C$ schéma des zéros d’une section non nulle de ${\mathcal {E}}(n)$ est une courbe minimale dans sa classe de biliaison.
LA - fre
KW - fiber bundle; biliaison; minimal curve; subcanonical curve
UR - http://eudml.org/doc/116001
ER -

References

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  8. M. Martin-Deschamps, D. Perrin, Sur la classification des courbes gauches, Astérisque Vol (1990), 184-185 Zbl0717.14017MR1073438
  9. M. Martin-Deschamps, D. Perrin, Quand un morphisme de fibrés dégénère-t-il le long d'une courbe lisse ?, 200 (1998, July), Marcel Dekker, Inc. MR1651093
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