Vanishing of sections of vector bundles on 0-dimensional schemes

Edoardo Ballico

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 403-411
  • ISSN: 0010-2628

Abstract

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Here we give conditions and examples for the surjectivity or injectivity of the restriction map H 0 ( X , F ) H 0 ( Z , F | Z ) , where X is a projective variety, F is a vector bundle on X and Z is a “general” 0 -dimensional subscheme of X , Z union of general “fat points”.

How to cite

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Ballico, Edoardo. "Vanishing of sections of vector bundles on 0-dimensional schemes." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 403-411. <http://eudml.org/doc/248442>.

@article{Ballico1999,
abstract = {Here we give conditions and examples for the surjectivity or injectivity of the restriction map $H^0(X,F)\rightarrow H^0(Z,F\,|\, Z)$, where $X$ is a projective variety, $F$ is a vector bundle on $X$ and $Z$ is a “general” $0$-dimensional subscheme of $X$, $Z$ union of general “fat points”.},
author = {Ballico, Edoardo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {zero-dimensional scheme; cohomology; vector bundle; fat point; zero-dimensional scheme; cohomology; vector bundle; fat point},
language = {eng},
number = {3},
pages = {403-411},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Vanishing of sections of vector bundles on 0-dimensional schemes},
url = {http://eudml.org/doc/248442},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Ballico, Edoardo
TI - Vanishing of sections of vector bundles on 0-dimensional schemes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 403
EP - 411
AB - Here we give conditions and examples for the surjectivity or injectivity of the restriction map $H^0(X,F)\rightarrow H^0(Z,F\,|\, Z)$, where $X$ is a projective variety, $F$ is a vector bundle on $X$ and $Z$ is a “general” $0$-dimensional subscheme of $X$, $Z$ union of general “fat points”.
LA - eng
KW - zero-dimensional scheme; cohomology; vector bundle; fat point; zero-dimensional scheme; cohomology; vector bundle; fat point
UR - http://eudml.org/doc/248442
ER -

References

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  1. Alexander J., Hirschowitz A., An asymptotic vanishing theorem for generic unions of multiple points, preprint alg-geom 9703037. Zbl0973.14026MR1756998
  2. Atiyah M.F., Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 514-452; reprinted in: Michael Atiyah Collected Works, Vol. l, pp.105-143, Oxford Science Publications, Clarendon Press, Oxford, 1988. (1957) Zbl0084.17305MR0131423
  3. Gimigliano A., Our thin knowledge of fat points, in: Queen's Papers in Pure and Applied Mathematics, vol. 83, The Curves Seminar at Queen's, Vol. VI, 1989. Zbl0743.14005MR1036032
  4. Hartshorne R., Hirschowitz A., Cohomology of a general instanton bundle, Ann. Scient. Ec. Norm. Sup. 15 (1982), 365-362. (1982) Zbl0509.14015MR0683638
  5. Hein G., Kurke H., Restricted tangent bundle of space curves, Israel Math. Conf. Proc. 9 (1996), 283-294. (1996) MR1360509
  6. Hirschowitz A., Problémes de Brill-Noether en rang supérieur, C.R. Acad. Sci. Paris, Série I, 307 (1988), 153-156. (1988) Zbl0654.14017MR0956606
  7. Hirschowitz A., Existence de faisceaux réflexifs de rang deux sur 𝐏 3 à bonne cohomologie, Publ. Math. I.H.E.S. 66 (1988), 105-137. (1988) MR0932136
  8. Hirschowitz A., Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles génériques, J. reine angew. Math. 397 (1989), 208-213. (1989) MR0993223
  9. Iarrobino A., Inverse systems of a symbolic power III: thin algebras and fat points, preprint, 1994. MR1473851
  10. Iarrobino A., Associated graded algebra of a Gorenstein Artin algebra, Mem. Amer. Math. Soc. 514, 1994. Zbl0793.13010MR1184062
  11. Neeman A., Weierstrass points in characteristic p , Invent. Math. 75 (1984), 359-376. (1984) Zbl0555.14009MR0732551
  12. Raynaud M., Sections des fibrés vectoriels sur les courbes, Bull. Soc. Math. France 110 (1982), 103-125. (1982) MR0662131

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