Open Access
2005 On the stability of the tangent bundle of a hypersurface in a Fano variety
Indranil Biswas, Georg Schumacher
J. Math. Kyoto Univ. 45(4): 851-860 (2005). DOI: 10.1215/kjm/1250281661

Abstract

Let MM be a complex projective Fano manifold whose Picard group is isomorphic to Z and the tangent bundle TM is semistable. Let ZM be a smooth hypersurface of degree strictly greater than degree(TM)(dimCZ1)/(2dimCZ1) and satisfying the condition that the inclusion of Z in M gives an isomorphism of Picard groups. We prove that the tangent bundle of Z is stable. A similar result is proved also for smooth complete intersections in M. The main ingredient in the proof of it is a vanishing result for the top cohomology of the twisted holomorphic differential forms on Z.

Citation

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Indranil Biswas. Georg Schumacher. "On the stability of the tangent bundle of a hypersurface in a Fano variety." J. Math. Kyoto Univ. 45 (4) 851 - 860, 2005. https://doi.org/10.1215/kjm/1250281661

Information

Published: 2005
First available in Project Euclid: 14 August 2009

zbMATH: 1097.14035
MathSciNet: MR2226634
Digital Object Identifier: 10.1215/kjm/1250281661

Subjects:
Primary: 14J45
Secondary: 14J60 , 14J70

Rights: Copyright © 2005 Kyoto University

Vol.45 • No. 4 • 2005
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