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On stability of tangent bundles of Fano manifolds with b_2=1

Thomas Peternell·Jaroslaw A. Wisniewski
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Abstract

In the present paper we discuss stability of the tanget bundle of a Fano n-fold of index >= n-2 and b_2=1. For example, we prove that all Fano 4-folds with b_2=1 have stable tangent bundle. For this purpose we prove some vanishing theorems for sheaves of twisted holomorphic forms on ample divisors and cyclic coverings of manifolds having "special cohomology".

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BibTeXRIS

Thomas Peternell, Jaroslaw A. Wisniewski. 1993-11-14. On stability of tangent bundles of Fano manifolds with b_2=1. https://arxiv.org/abs/alg-geom/9306010

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