论文标题
在建筑物和对称差速器中的pluriharmonic地图
Pluriharmonic maps into buildings and symmetric differentials
论文作者
论文摘要
给定一个复杂的平滑准标记品种$ x $，是在某些非Archimedean本地字段$ k $和zariski密集表示$ \ varrho：π_1（x）\ g（k）$上定义的半半密度代数$ g $，我们构建了$ \ equiriains $ - equirian norm-earmonic（x） Bruhat-tits建立$δ$ g $的$δ（g）$，具有一些合适的渐近行为。该定理将Gromov-Schoen的先前工作概括为准标记设置。 作为一个应用程序，我们证明，如果存在线性表示$π_1（x）\ to {\ rm gl} _n（\ mathbb {k}）$，则具有无限映像，其中$ \ mathbb {k {k} $。该定理将Brunebarbe，Klingler和Totaro的先前工作概括为准标准设置。
Given a complex smooth quasi-projective variety $X$, a semisimple algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:π_1(X)\to G(K)$, we construct a $\varrho$-equivariant (pluri-)harmonic map from the universal cover of $X$ into the Bruhat-Tits building $Δ(G)$ of $G$, with some suitable asymptotic behavior. This theorem generalizes the previous work by Gromov-Schoen to the quasi-projective setting. As an application, we prove that $X$ has nonzero global logarithmic symmetric differentials if there exists a linear representation $π_1(X)\to {\rm GL}_N(\mathbb{K})$ with infinite image, where $ \mathbb{K}$ is any field. This theorem generalizes the previous work by Brunebarbe, Klingler and Totaro to the quasi-projective setting.
