Real structures on torus bundles and their deformations

Deformations of the tangent bundle of projective manifolds

We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.

Isomonodromic deformations of logarithmic connections and stable parabolic vector bundles

We consider irreducible logarithmic connections $(E,\,δ)$ over compact Riemann surfaces $X$ of genus at least two. The underlying vector bundle $E$ inherits a natural parabolic structure over the singular locus of the connection $δ$; the parabolic structure is given by the residues of $δ$. We prove that for the universal isomonodromic deformation of the triple $(X,\,E,\,δ)$, the parabolic vector bundle corresponding to a generic parameter in the Teichmüller space is parabolically stable. In the case of parabolic vector bundles of rank two, the general parabolic vector bundle is even parabolica…

Calabi-Yau流形与全纯向量丛联合形变的Kuranishi空间

The Kuranishi space of joint deformations of Calabi--Yau manifolds and holomorphic vector bundles

本文研究Calabi-Yau流形与全纯向量丛的联合形变，在Fujiki流形等条件下证明无阻碍性，并构造有阻碍的例子，推广了Li-Pan和Iacono-Manetti定理，回答了Felten的两个问题。

The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces

We introduce a way of presentation of pairs $(E,\nabla)$, where $E$ is a bundle on a Riemann surface and $\nabla$ is a logarithmic connection in $E$, which is based on a presentation of the surface as a factor of the exterior of the unit disc. In this presentation we write the local equation of isomonodormic deformation of pairs $(E,\nabla)$. These conditions are written as a modified Schlesinger system on a Riemann sphere (and in the typical case just as an ordinary Schlesinger system) plus some linear system.