自对偶规范场、全纯丛和上同调集的模空间

关于transmittal全纯向量场的全纯等变上同调

Holomorphic Equivariant Cohomology via a Transversal Holomorphic Vector Field

本文给出了Bismut定理的一个推广的解析证明（[Bis 1，定理5.1]），即当$v$是紧致复流形$X$上具有零点集$Y$的横截全纯向量场时，嵌入$j:Y\to X$诱导了$X$通过$v$的全纯等变上同调与Dolbeault之间的自然同构，其中系数在$ξ$中系数在$ξ|_Y$中的$Y$的上同调，其中$ξ\to X$是$X$上的全纯向量丛。

Poisson Cohomology of holomorphic toric Poisson manifolds. II

In this paper, we give a description of holomorphic multi-vector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties. Based on the result, we compute the Poisson cohomology groups of holomorphic toric Poisson manifolds, i.e., toric varieties endowed with $T$-invariant holomorphic Poisson structures.

Poisson Cohomology of holomorphic toric Poisson manifolds. I

A holomorphic toric Poisson manifold is a nonsingular toric variety equipped with a holomorphic Poisson structure, which is invariant under the torus action. In this paper, we computed the Poisson cohomology groups for all holomorphic toric Poisson structures on $CP^n$, with the stand Poisson structure on $CP^n$ as a special case. We also computed the algebraic and the formal Poisson cohomology groups of holomorphic toric Poisson structures on $C^n$.

Super $J$-holomorphic Curves: Construction of the Moduli Space

Let $M$ be a super Riemann surface with holomorphic distribution $\mathcal{D}$ and $N$ a symplectic manifold with compatible almost complex structure $J$. We call a map $Φ\colon M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$. Such a super $J$-holomorphic curve is a critical point for the superconformal action and satisfies a super differential equation of first order. Using component fields of this super differential equation and a transversality argument we construct the moduli space of super $J$-holomorphic curves as a smoo…

全纯Poisson流形与全纯李代数胚

Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

本文从实Poisson几何的角度研究了全纯Poisson流形和全纯李代数胚。利用Magri-Morosi的Poisson Nijenhuis结构给出了全纯Poisson结构的一个特征，并描述了一个计算全纯Poisson上同调的二重复形.证明了向量丛$A\to X$上的全纯李代数胚结构等价于一对匹配的复李代数胚$(T^{0,1}X,A^{1,0})$，在Lu意义下. $A$的全纯李代数胚上同调同构于椭圆李代数胚$T^{0,1}X\bowtie A^{1,0}$的上同调。当$(X,π)$是一个全纯Poisson流形且$A=(T^*X)_π$时，这样的椭圆李代数体与对应于全纯Poisson流形的广义复结构的Dirac结构一致。

星形中岛奎弗簇、抛物希格斯丛模空间及其全纯辛结构

Star-Shaped Nakajima Quiver Varieties, Parabolic Higgs Bundle Moduli Spaces, and their Holomorphic Symplectic Structures

本文构造了从星形中岛奎弗簇到中心Levi抛物希格斯丛模空间的映射，证明其保持稳定性并同胚于具有平凡底层全纯结构的希格斯丛轨迹，进而证明该映射识别了两个空间上的自然全纯辛结构。