论文标题
在非紧凑型riemann表面上的普通半岛式希格斯捆绑的谐波指标
Harmonic metrics of generically regular semisimple Higgs bundles on non-compact Riemann surfaces
论文作者
论文摘要
我们证明，在任何riemann表面上配备了非脱位对称配对的普通的常规半神经捆绑包总是与配对兼容的谐波度量。我们还研究了这种兼容的谐波指标的分类，在riemann表面是紧凑的riemann表面中有限集合$ d $的补充的情况下。特别是，如果Higgs捆绑包是野生且常规的半岛，我们证明了兼容的谐波度量的独特性。
We prove that a generically regular semisimple Higgs bundle equipped with a non-degenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such compatible harmonic metrics in the case where the Riemann surface is the complement of a finite set $D$ in a compact Riemann surface. In particular, we prove the uniqueness of a compatible harmonic metric if the Higgs bundle is wild and regular semisimple at each point of $D$.
