Fibrés uniformes de rang élevé sur ℙ 2

Georges Elencwajg

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 4, page 89-114
  • ISSN: 0373-0956

Abstract

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A holomorphic vector bundle on P 2 is said to be uniform if its pull-backs by all linear embeddings P 1 → P 2 are isomorphic. We classify uniform bundles of rank 4 on P 2 .

How to cite

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Elencwajg, Georges. "Fibrés uniformes de rang élevé sur ${\mathbb {P}}_2$." Annales de l'institut Fourier 31.4 (1981): 89-114. <http://eudml.org/doc/74519>.

@article{Elencwajg1981,
abstract = {Un fibré vectoriel holomorphe sur $\{\bf P\}_2$ est dit uniforme si ses images réciproques sous tous les plongements linéaires $\{\bf P\}_1 \rightarrow \{\bf P\}_2$ sont isomorphes. Nous classons les fibrés uniformes de rang 4 sur $\{\bf P\}_2$.},
author = {Elencwajg, Georges},
journal = {Annales de l'institut Fourier},
keywords = {splitting type of uniform vector bundle of rank 4},
language = {fre},
number = {4},
pages = {89-114},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fibrés uniformes de rang élevé sur $\{\mathbb \{P\}\}_2$},
url = {http://eudml.org/doc/74519},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Elencwajg, Georges
TI - Fibrés uniformes de rang élevé sur ${\mathbb {P}}_2$
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 4
SP - 89
EP - 114
AB - Un fibré vectoriel holomorphe sur ${\bf P}_2$ est dit uniforme si ses images réciproques sous tous les plongements linéaires ${\bf P}_1 \rightarrow {\bf P}_2$ sont isomorphes. Nous classons les fibrés uniformes de rang 4 sur ${\bf P}_2$.
LA - fre
KW - splitting type of uniform vector bundle of rank 4
UR - http://eudml.org/doc/74519
ER -

References

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  1. [1] J. M. DREZET, Fibrés uniformes sur P2, Thèse 3e cycle, (1980). Zbl0456.14012
  2. [2] G. ELENCWAJG, Les fibrés uniformes de rang 3 sur P2(C) sont homogènes, Math. Ann., 231 (1978), 217-227. Zbl0378.14003MR58 #1278
  3. [3] G. ELENCWAJG, Des fibrés uniformes non homogènes, Math. Ann., 239 (1979), 185-192. Zbl0498.14007MR80k:32030
  4. [4] G. ELENCWAJG, Thèse de Doctorat d'État, Nice (1979). 
  5. [5] G. ELENCWAJG et O. FORSTER, Bounding Cohomology groups of Vector Bundles on Pn, Math. Ann., 246 (1980), 251-270. Zbl0432.14011MR81h:32035
  6. [6] G. ELENCWAJG, A. HIRSCHOWITZ et M. SCHNEIDER, Les fibrés uniformes de rang au plus n sur Pn(C) sont ceux qu'on croit, Proceedings of the Nice Conference 1979 on Vector Bundles and Differential equations, Birkhäuser, Boston, 1980. Zbl0456.32009MR81k:14015
  7. [7] R. HARTSHORNE, Algebraic Geometry. Graduate texts in mathematics, Vol. 52, Berlin, Heidelberg, New-York, Springer-Verlag, 1977. Zbl0367.14001MR57 #3116
  8. [8] F. HIRZEBRUCH, Topological Methods in Algebraic Geometry, 3rd ed. Berlin, Heidelberg, New-York. Springer Verlag 1966. Zbl0138.42001MR34 #2573
  9. [9] S. KLEIMAN, The enumerative theory of singularities, Real and Complex Singularities, Oslo 1976, Sÿthoff et Noordhoof (1977). Zbl0385.14018
  10. [10] C. OKONEK, M. SCHNEIDER et H. SPINDLER, Vector Bundles on Complex Projective Spaces, Progress in Mathematics, 3, Boston, Basel, Stuttgart, Birkhäuser, 1980. Zbl0438.32016MR81b:14001
  11. [11] H. SPINDLER, Der Satz von Grauert-Mülich für beliebige semistabile holomorphe Vektorraumbündel über dem n-dimensionalen komplex-projektiven Raum, Math. Ann., 243 (1979), 131-141. Zbl0435.32018MR81b:14008
  12. [12] A. VAN DE VEN. On uniform vector bundles, Math. Ann., 195 (1972), 246-248. Zbl0215.43202MR45 #276

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