Submanifolds with splitting tangent sequence

Splitting submanifolds of families of fake elliptic curves

Let N a compact complex submanifold of a compact complex manifold M. We say N splits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok a splitting submanifold of a Kaehler Einstein manifold with a projective structure is totally geodesic. The classification of all splitting submanifolds of families of fake elliptic curves given here completes the case of threefolds M with a projective structure by a previous result of the authors.

Projective manifolds with splitting tangent bundles, I

We investigate the universal cover of projective threefolds whose tangent bundle is a direct sum of subbundles in case the Kodaira dimension is not 1 and 2. We also prove results on Fano manifolds with splitting tangent bundles in any dimension.

在 Picard 数为一的有理齐性空间中分裂子流形

Splitting submanifolds in rational homogeneous spaces of Picard number one

在 Picard 数为一的有理齐性空间中，研究分裂子流形的分类及其性质，利用全局全纯向量场建立新的分类方法。

PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle

We give an explicit parametrization of the Hilbert schemes of rational curves C in P^n having a given splitting type of the restricted tangent bundle from P^n to C. The adopted technique uses the description of such curves as projections of a rational normal curve from a suitable linear vertex and a classification of those vertices that correspond to the required splitting type of the restricted tangent bundle. This classification involves the study of a suitable PGL(2) action on the relevant Grassmannian variety.

On plane rational curves and the splitting of the tangent bundle

Given an immersion $ϕ: P^1 \to ¶^2$, we give new approaches to determining the splitting of the pullback of the cotangent bundle. We also give new bounds on the splitting type for immersions which factor as $ϕ: P^1 \cong D \subset X \to P^2$, where $X \to P^2$ is obtained by blowing up $r$ distinct points $p_i \in P^2$. As applications in the case that the points $p_i$ are generic, we give a complete determination of the splitting types for such immersions when $r \leq 7$. The case that $D^2=-1$ is of particular interest. For $r \leq8$ generic points, it is known that there are only finitely m…

具有局部自由切 sheaf 的全纯分布的分解特性

Splitting aspects of holomorphic distributions with locally free tangent sheaf

本文研究全纯分布的分解特性，通过局部自由切 sheaf 的条件，探讨其在不同复流形上的分解可能性及应用。