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


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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References:

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[2] D. Gieseker : On the Moduli of Vector Bundles on an Algebraic Surface , preprint. · Zbl 0381.14003 · doi:10.2307/1971157
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[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
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[8] A. Grothendieck : Sur la classification des fibrés holomorphes sur la sphère de Riemann . Am. J. Math. 79 (1957) 121-138. · Zbl 0079.17001 · doi:10.2307/2372388
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[11] S. Kleiman : Toward a Numerical Theory of Ampleness . Ann. of Math. 84 (1966) 292-343. · Zbl 0146.17001 · doi:10.2307/1970447
[12] S. Langton : Valuative Criteria for Vector Bundles . Ann. of Math. 101 (1975) 88-111. · Zbl 0307.14007 · doi:10.2307/1970987
[13] M. Maruyama : Openness of a family of torsion-free sheaves , preprint. · Zbl 0404.14004 · doi:10.1215/kjm/1250522875
[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 · doi:10.2307/1970710
[16] F. Takemoto : Stable Vector Bundles on an Algebraic Surface . Nagoya Math J. (1972). · Zbl 0245.14007 · doi:10.1017/S0027763000014896
[17] A. Tjurin : Classification of Vector Fiberings over an Algebraic Curve of Arbitrary Genus . Amer. Math. Soc. Transl. (2) 63 (1967). · Zbl 0207.51603 · doi:10.1090/trans2/063/07
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