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A Generalisation of Nagata's Theorem on Ruled Surfaces

Published online by Cambridge University Press:  04 December 2007

Yogish I. Holla  and
M. S. Narasimhan
Yogish I. Holla
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India. E-mail: [email protected]
M. S. Narasimhan
Affiliation:
ICTP, PO Box 586, Strada Costiera 11, Miramare, I-34100, Italy
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Abstract

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We prove a generalisation of a theorem of Nagata on ruled surface to the case of the fiber bundle E/P → X, associated to a principal G-bundle E. Using this we prove boundedness for the isomorphism classes of semi-stable G-bundles in all characteristics.

Keywords

Principal bundlesAlgebraic curvesReductive algebraic groups
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 3 , July 2001 , pp. 321 - 332
Copyright
© 2001 Kluwer Academic Publishers