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An analogue of Langton's theorem on valuative criteria for vector bundles

Published online by Cambridge University Press:  14 November 2011

V. B. Mehta  and
A. Ramanathan
V. B. Mehta
Affiliation:
Department of Mathematics, University of Bombay, Kalina, Bombay 400 098, India
A. Ramanathan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
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Synopsis

We prove in this paper that on a non-singular projective variety, the χ-semistable functor is proper and the χ-stable functor is separated. This result was proved for μ-stability and μ-semistability by Langton. An essential part of our proof consists in defining a notion of stability between the μ and χ definitions and then proceeding by induction.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 39 - 45
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Gieseker, D.. On the moduli of vector bundles on an algebraic surface. Ann. of Math. 106 (1977), 45–60.CrossRefGoogle Scholar
2Grothendieck, A.. Techniques de descente et theoremes d'existence en geometrie algebrique I. Seminaire Bourbaki 1959/1960, No. 190.Google Scholar
3Grothendieck, A.. Techniques de construction et theoremes d'existence en geometrie algebrique IV, Les schemes de Hilbert. Seminaire Bourbaki 1960/1961, No. 221.Google Scholar
4Langton, S.. Valuative criteria for families of vector bundles on algebraic varieties. Ann. of Math. 101 (1975), 88–110.CrossRefGoogle Scholar
5Maruyama, M.. On the moduli of stable sheaves I. J. Math. Kyoto Univ. 17 (1977), 91–126.Google Scholar
6Maruyama, M.. Moduli of stable sheaves II. J. Math. Kyoto Univ. 18 (1978), 557–614.Google Scholar
7Mehta, V. and Seshadri, C. S.. Moduli of vector bundles on curves with parabolic structures. Math. Ann. 248 (1980), 205–239.CrossRefGoogle Scholar
8Takemoto, F.. Stable vector bundles on an algebraic surface. Nagoya Math. J. 47 (1972), 29–48.CrossRefGoogle Scholar