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Shatz, Stephen S.

The decomposition and specialization of algebraic families of vector bundles. (English) Zbl 0371.14010

Compos. Math. 35, 163-187 (1977).
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Cited in 53 Documents

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14M99 Special varieties
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14C05 Parametrization (Chow and Hilbert schemes)
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\textit{S. S. Shatz}, Compos. Math. 35, 163--187 (1977; Zbl 0371.14010)
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References:

[1] M.F. Atiyah : Vector Bundles over an Elliptic Curve . Proc. Lond. Math. Soc. 7 (1957) 414-452. · Zbl 0084.17305
[2] D. Gieseker : On the Moduli of Vector Bundles on an Algebraic Surface , preprint. · Zbl 0381.14003
[3] A. Grothendieck and J. Dieudonné : Éléments de Géométrie Algébrique , 4. Pub. Math. I.H.E.S., 24, 1965. · Zbl 0135.39701
[4] A. Grothendieck and J. Dieudonné : Éléments de Géométrie Algebrique , 2. Pub. Math. I.H.E.S., 8, 1961. |
[5] A. Grothendieck and J. Dieudonné : Éléments de Géométrie Algébrique , 2. · Zbl 0227.14001
[6] A. Grothendieck and J. Dieudonné : Éléments de Géométrie Algébrique , 3. Pub. Math. I.H.E.S., 17, 1963. · Zbl 0122.16102
[7] A. Grothendieck and J. Dieudonné : Éléments de Géométrie Algébrique , 4, Pub. Math. I.H.E.S., 28, 1966. · Zbl 0144.19904
[8] A. Grothendieck : Sur la classification des fibrés holomorphes sur la sphère de Riemann . Am. J. Math. 79 (1957) 121-138. · Zbl 0079.17001
[9] A. Grothendieck : Techniques de Construction en Géométrie Algébrique IV . Sem. Bourb. 221 (1961). · Zbl 0236.14003
[10] G. Harder and M. Narasimhan : On the Cohomology Groups of Moduli Spaces of Vector Bundles on Curves . Math. Ann. 212 (1975) 215-248. · Zbl 0324.14006
[11] S. Kleiman : Toward a Numerical Theory of Ampleness . Ann. of Math. 84 (1966) 292-343. · Zbl 0146.17001
[12] S. Langton : Valuative Criteria for Vector Bundles . Ann. of Math. 101 (1975) 88-111. · Zbl 0307.14007
[13] M. Maruyama : Openness of a family of torsion-free sheaves , preprint. · Zbl 0404.14004
[14] D. Mumford : Projective Invariants of Projective Structures and Applications . Proc. Stockholm Cong., 1962, 526-530. · Zbl 0154.20702
[15] M. Narasimhan and C.S. Seshadri : Stable and Unitary Vector Bundles on a Compact Riemann Surface . Ann. of Math. 82 (1965) 540-567. · Zbl 0171.04803
[16] F. Takemoto : Stable Vector Bundles on an Algebraic Surface . Nagoya Math J. (1972). · Zbl 0245.14007
[17] A. Tjurin : Classification of Vector Fiberings over an Algebraic Curve of Arbitrary Genus . Amer. Math. Soc. Transl. (2) 63 (1967). · Zbl 0207.51603
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