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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

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