Bundle homogeneity and holomorphic connections

The Drinfeld Sokolov Holomorphic Bundle and Classical

Lagrangian Sections and Holomorphic U(1)-connections

It was conjectured in [SYZ] that Calabi-Yau spaces can be often fibered by special Lagrangian tori and their mirrors can be constructed by dualizing these tori. It was further suggested by Vafa in [V] that the holomorphic vector bundles on a Calabi-Yau n-fold M correspond to the Lagrangian submanifolds in the mirror M̌ and the stable vector bundles correspond to the special Lagrangian submanifol...

Holomorphic Connections on Filtered Bundles over Curves

Let X be a compact connected Riemann surface and EP a holomorphic principal P–bundle over X , where P is a parabolic subgroup of a complex reductive affine algebraic group G. If the Levi bundle associated to EP admits a holomorphic connection, and the reduction EP ⊂ EP × P G is rigid, we prove that EP admits a holomorphic connection. As an immediate consequence, we obtain a sufficient condition...

Holomorphic Affine Connections on Non-kähler Manifolds

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In particular, if the geometric structure is rigid in Gromov’s sense, then the ...

On the Canonical Line Bundle and Negative Holomorphic Sectional Curvature

We prove that a smooth complex projective threefold with a Kähler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef dimension of the canonical line bundle is maximal. With certain additional assumptions, ampleness is again obtained. The methods used come from both complex differen...