Abstract
Let MM be a complex projective Fano manifold whose Picard group is isomorphic to Z and the tangent bundle TM is semistable. Let Z⊂M be a smooth hypersurface of degree strictly greater than degree(TM)(dimCZ−1)/(2dimCZ−1) 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
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
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