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

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".

17 pages and 2 tables, plain TeX, Forschungsschwerpunkt Komplexe Mannigfaltigkeiten, heft nr. 174, Bayreuth 1993

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