Holonomy groups of stable vector bundles

On the algebraic holonomy of stable principal bundles

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 Kähler--Einstein metric, then the algebraic holonomy of $TM$ is ${\rm GL}(n, {\mathbb C})$.

Hypercomplex manifolds with trivial canonical bundle and their holonomy

Let (M,I,J,K) be a compact hypercomplex manifold admitting an HKT-metric. Assume that the canonical bundle of (M,I) is trivial as a holomorphic line bundle. We show that the holonomy of Obata connection on M is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds equipped with abelian hypercomplex structures, showing that such manifolds have holonomy in SL(n,H).

Fano超曲面上具有稳定或半稳定法丛的曲线

Holonomy and bundle stability for curves on Fano hypersurfaces

本文证明了在Fano超曲面及射影空间中，存在具有稳定或半稳定法丛的曲线，推广了先前仅限于特定环境空间的结果。

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.

Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2

We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of framed instantons on $\R^4$, called the space of twistor sections. We then use this characterization to prove that $M$ is equipped with a torsion-free affine connection with holonomy in $Sp(2n,\C)$.