Remarks on Seshadri constants of vector bundles

Christopher Hacon

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 3, page 767-780
  • ISSN: 0373-0956

Abstract

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We give a lower bound for the Seshadri constants of ample vector bundles which depends only on the numerical properties of the Chern classes and on a “stability” condition.

How to cite

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Hacon, Christopher. "Remarks on Seshadri constants of vector bundles." Annales de l'institut Fourier 50.3 (2000): 767-780. <http://eudml.org/doc/75437>.

@article{Hacon2000,
abstract = {We give a lower bound for the Seshadri constants of ample vector bundles which depends only on the numerical properties of the Chern classes and on a “stability” condition.},
author = {Hacon, Christopher},
journal = {Annales de l'institut Fourier},
keywords = {Seshadri constants; ample vector bundles; spanned vector bndles; stability of vector bundles},
language = {eng},
number = {3},
pages = {767-780},
publisher = {Association des Annales de l'Institut Fourier},
title = {Remarks on Seshadri constants of vector bundles},
url = {http://eudml.org/doc/75437},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Hacon, Christopher
TI - Remarks on Seshadri constants of vector bundles
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 3
SP - 767
EP - 780
AB - We give a lower bound for the Seshadri constants of ample vector bundles which depends only on the numerical properties of the Chern classes and on a “stability” condition.
LA - eng
KW - Seshadri constants; ample vector bundles; spanned vector bndles; stability of vector bundles
UR - http://eudml.org/doc/75437
ER -

References

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  1. [1] E. BALLICO, Spanned and ample vector bundles with low Chern numbers, Pacific Journal of Mathematics, 140, 2 (1989), 209-216. Zbl0638.14010MR90j:14023
  2. [2] E. BALLICO, On ample and spanned rank-3 vector bundles with low Chern numbers, Manuscripta Math., 68 (1990), 9-16. Zbl0717.14011MR91g:14037
  3. [3] M. BELTRAMETTI, A. SOMMESE, S. SCHNEIDER, Chern inequalities and spannedness of the adjoint bundle, Proceedings of the Hirzebruch Conference on Algebraic Geometry (Ramat Gan, 1993), 97-107, Israel Math. Conf. Proc., 9, Bar-Ilan Univ., Ramat Gan, 1996. Zbl0870.14009
  4. [4] M. BELTRAMETTI, A. SOMMESE, S. SCHNEIDER, Applications of the Ein-Lazars-feld criterion for spannedness of adjoint bundles, Mathematische Zeitschrift, 214 (1993), 593-599. Zbl0804.14006
  5. [5] M. de CATALDO, Effective non-vanishing, effective global generation, Preprint alggeom/9708004. Zbl0934.14002
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  7. [7] L. EIN, R. LAZARSFELD, Seshadri constants on smooth surfaces, Journées de Géométrie Algébrique d'Orsay (Orsay, 1992), Astérisque n° 218 (1993), 177-186. Zbl0812.14027MR95f:14031
  8. [8] L. EIN, R. LAZARSFELD, M. NAKAMAYE, Zero-estimates, intersection theory, and a theorem of Demailly, Higher-dimensional complex varieties (Trento, 1994), 183-207, de Gruyter, Berlin, 1996. Zbl0892.14007
  9. [9] L. EIN, O. KÜCHLE, R. LAZARSFELD, Local positivity of ample line bundles, Jour. of Diff. Geo., 42 (1995), 193-219. Zbl0866.14004MR96m:14007
  10. [10] D. GIESEKER, P-Ample Bundles and their Chern Classes, Nagoya Math. J., Vol. 43 (1971), 91-116. Zbl0221.14010MR45 #5139
  11. [11] C. D. HACON, Examples of spanned and ample vector bundles with small numerical invariants, C.R.A.S. Paris, Série I Math., 323, n° 9 (1996), 1025-1029. Zbl0867.14007MR98c:14036
  12. [12] R. HARTSHORNE, Ample vector bundles, Publ. Math. IHES, 29 (1969), 63-94. Zbl0173.49003MR33 #1313
  13. [13] R. HARTSHORNE, Ample subvarieties of algebraic varieties, Springer Verlag, Lecture Notes in Mathematics, 156 (1970). Zbl0208.48901MR44 #211
  14. [14] R. HARTSHORNE, Ample vector bundles on curves, Nagoya Math. J., Vol. 43 (1971), 73-89. Zbl0218.14018MR45 #1929

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