对数 $\u001b[31m\mathfrak{sl}_2\u001b[0m$-联络的阿贝尔化

伴随判别式的对数导子

Logarithmic Derivations of Adjoint Discriminants

本文揭示了射影对偶性与沿射影空间约化因子D的对数向量场层之间的关系，并针对简单李群的伴随判别式D，研究了其对数模的结构，给出了单李型和非单李型情况下的自由分解。

Sheaves of bounded $p$-adic logarithmic differential forms

Let $K$ be a local field, $X$ the Drinfel'd symmetric space $X$ of dimension $d$ over $K$ and ${\mathfrak X}$ the natural formal ${\mathcal O}_K$-scheme underlying $X$; thus $G={\rm GL}\sb {d+1}(K)$ acts on $X$ and ${\mathfrak X}$. Given a $K$-rational $G$-representation $M$ we construct a $G$-equivariant subsheaf ${\mathcal M}^0_{{\mathcal O}_{\dot{K}}}$ of ${\mathcal O}_K$-lattices in the constant sheaf $M$ on ${\mathfrak X}$. We study the cohomology of sheaves of logarithmic differential forms on $X$ (or ${\mathfrak X}$) with coefficients in ${\mathcal M}^0_{{\mathcal O}_{\dot{K}}}$. In the…

关于对数微分系统的单值映射

On the monodromy map for the logarithmic differential systems

本文研究对数微分系统的单值映射，证明在特定亏格和维数条件下该映射为浸入，并给出非浸入条件，推广了非奇异情形的结果。

等变抛物联络与根栈

Equivariant Parabolic connections and stack of roots

本文研究了线性代数群作用下的等变抛物联络，证明了群作用可自然提升至根栈，并建立了根栈上等变对数联络范畴与原簇上等变抛物联络范畴的等价关系。

根栈上的实结构与抛物联络

Real Structures on Root Stacks and Parabolic Connections

本文研究带实结构的光滑复代数簇上根栈的实化问题，证明在反全纯对合保持除子不变的条件下根栈自然具有相容实结构，并建立实对数联络与实抛物联络的范畴等价。

Moduli space of logarithmic connections singular over a finite subset of a compact Riemann surface

Let $S$ be a finite subset of a compact connected Riemann surface $X$ of genus $g \geq 2$. Let $\cat{M}_{lc}(n,d)$ denote the moduli space of pairs $(E,D)$, where $E$ is a holomorphic vector bundle over $X$ and $D$ is a logarithmic connection on $E$ singular over $S$, with fixed residues in the centre of $\mathfrak{gl}(n,\C)$, where $n$ and $d$ are mutually corpime. Let $L$ denote a fixed line bundle with a logarithmic connection $D_L$ singular over $S$. Let $\cat{M}'_{lc}(n,d)$ and $\cat{M}_{lc}(n,L)$ be the moduli spaces parametrising all pairs $(E,D)$ such that underlying vector bundle $E$ …