On the algebraic holonomy of stable principal bundles

Details On the algebraic holonomy of stable principal bundles On the algebraic holonomy of stable principal bundles

2007-03-05

arxiv.org/abs/math/0703104v2

Mathematics

Algebraic Geometry

International Journal of Mathematics (to appear)

Scientific paper

Apart from math.AG/0608569, it contains the following applications of it. Let M be a simply connected, irreducible smooth complex projective variety of dimension $n$ such that the Picard number of $M$ is one. If the canonical line bundle $K_M$ is ample, then the algebraic holonomy of $TM$ is $\text{GL}(n, {\mathbb C})$. If $K^{-1}_M$ is ample, $\text{rank}(\text{NS}(M)) = 1$, the biholomorphic automorphism group of $M$ is finite, and $M$ admits a K\"ahler--Einstein metric, then the algebraic holonomy of $TM$ is ${\rm GL}(n, {\mathbb C})$.

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