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

Mathematics – Algebraic Geometry

Scientific paper

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

Scientific paper

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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