The decomposition and specialization of algebraic families of vector bundles

Stephen S. Shatz

Compositio Mathematica (1977)

  • Volume: 35, Issue: 2, page 163-187
  • ISSN: 0010-437X

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Shatz, Stephen S.. "The decomposition and specialization of algebraic families of vector bundles." Compositio Mathematica 35.2 (1977): 163-187. <http://eudml.org/doc/89345>.

@article{Shatz1977,
author = {Shatz, Stephen S.},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {163-187},
publisher = {Noordhoff International Publishing},
title = {The decomposition and specialization of algebraic families of vector bundles},
url = {http://eudml.org/doc/89345},
volume = {35},
year = {1977},
}

TY - JOUR
AU - Shatz, Stephen S.
TI - The decomposition and specialization of algebraic families of vector bundles
JO - Compositio Mathematica
PY - 1977
PB - Noordhoff International Publishing
VL - 35
IS - 2
SP - 163
EP - 187
LA - eng
UR - http://eudml.org/doc/89345
ER -

References

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  1. [1] M.F. Atiyah: Vector Bundles over an Elliptic Curve. Proc. Lond. Math. Soc.7 (1957) 414-452. Zbl0084.17305MR131423
  2. [2] D. Gieseker: On the Moduli of Vector Bundles on an Algebraic Surface, preprint. Zbl0381.14003MR466475
  3. [3] A. Grothendieck and J. Dieudonné: Éléments de Géométrie Algébrique, 4. Pub. Math. I.H.E.S., 24, 1965. Zbl0135.39701MR199181
  4. [4] A. Grothendieck and J. Dieudonné: Éléments de Géométrie Algebrique, 2. Pub. Math. I.H.E.S., 8, 1961. 
  5. [5] A. Grothendieck and J. Dieudonné: Éléments de Géométrie Algébrique, 2. Zbl0227.14001
  6. [6] A. Grothendieck and J. Dieudonné: Éléments de Géométrie Algébrique, 3. Pub. Math. I.H.E.S., 17, 1963. Zbl0122.16102MR163911
  7. [7] A. Grothendieck and J. Dieudonné: Éléments de Géométrie Algébrique, 4, Pub. Math. I.H.E.S., 28, 1966. Zbl0144.19904MR217086
  8. [8] A. Grothendieck: Sur la classification des fibrés holomorphes sur la sphère de Riemann. Am. J. Math.79 (1957) 121-138. Zbl0079.17001MR87176
  9. [9] A. Grothendieck: Techniques de Construction en Géométrie Algébrique IV. Sem. Bourb.221 (1961). Zbl0236.14003
  10. [10] G. Harder and M. Narasimhan: On the Cohomology Groups of Moduli Spaces of Vector Bundles on Curves. Math. Ann.212 (1975) 215-248. Zbl0324.14006MR364254
  11. [11] S. Kleiman: Toward a Numerical Theory of Ampleness. Ann. of Math.84 (1966) 292-343. Zbl0146.17001MR206009
  12. [12] S. Langton: Valuative Criteria for Vector Bundles. Ann. of Math.101 (1975) 88-111. Zbl0307.14007MR364255
  13. [13] M. Maruyama: Openness of a family of torsion-free sheaves, preprint. Zbl0404.14004MR429899
  14. [14] D. Mumford: Projective Invariants of Projective Structures and Applications. Proc. Stockholm Cong., 1962, 526-530. Zbl0154.20702MR175899
  15. [15] M. Narasimhan and C.S. Seshadri: Stable and Unitary Vector Bundles on a Compact Riemann Surface. Ann. of Math.82 (1965) 540-567. Zbl0171.04803MR184252
  16. [16] F. Takemoto: Stable Vector Bundles on an Algebraic Surface. Nagoya Math J. (1972). Zbl0245.14007MR337966
  17. [17] A. Tjurin: Classification of Vector Fiberings over an Algebraic Curve of Arbitrary Genus. Amer. Math. Soc. Transl. (2) 63 (1967). Zbl0207.51603

Citations in EuDML Documents

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  1. A. Bruguières, The scheme of morphisms from an elliptic curve to a Grassmannian
  2. Laurent Bruasse, Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion
  3. Laurent Bruasse, Andrei Teleman, Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
  4. Laurent Bruasse, Optimal destabilizing vectors in some Gauge theoretical moduli problems
  5. André Hirschowitz, Sur la restriction des faisceaux semi-stables
  6. J.-M. Drezet, J. Le Potier, Fibrés stables et fibrés exceptionnels sur 2
  7. Chris Woodward, Moment maps and geometric invariant theory
  8. Chris Woodward, Moment maps and geometric invariant theory—Corrected version (October 2011)

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