Semistability and Restrictions of Tangent Bundle to Curves
نویسنده
چکیده
We consider all complex projective manifolds X that satisfy at least one of the following three conditions: (1) There exists a pair (C , φ), where C is a compact connected Riemann surface and φ : C −→ X a holomorphic map, such that the pull back φ∗TX is not semistable. (2) The variety X admits an étale covering by an abelian variety. (3) The dimension dimX ≤ 1. We prove that the following classes are among those that are of the above type. • All X with a finite fundamental group. • All X such that there is a nonconstant morphism from CP to X . • All X such that the canonical line bundle KX is either positive or negative or c1(KX) ∈ H (X, Q) vanishes. • All X with dimC X = 2.
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