On the algebraic holonomy of stable principal bundles

Abstract

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 $K_M^{-1}$ is ample, $\text{rank}(\text{NS}(M))=1$, the biholomorphic automorphism group of $M$ is finite, and $M$ admits a Kähler--Einstein metric, then the algebraic holonomy of $TM$ is $\mathrm{GL}(n,\mathbb{C})$.

International Journal of Mathematics (to appear)