标题： 实Bialynicki-Birula流在Higgs丛模空间中 显示英文标题

标题： Real Bialynicki-Birula flows in moduli spaces of Higgs bundles

摘要： 设$X$为一个亏格为$\geqslant 2$的紧致黎曼曲面$X$，并设$\sigma:X \to X$为一个反全纯对合。 使用实和四元数Hodge丛系统，我们研究了在诱导实结构$(E,\phi) \to (\sigma^*(\overline{E}),\sigma^*(\overline{\phi}))$下，半稳定Higgs丛的模空间的实点集$\mathbb{R} \mathbf{M}_{\mathrm{Dol}}(r,d)$的拓扑性质，该模空间的秩为$r$，次数为$d$，定义在$X$上。 我们特别证明了当$\mathrm{gcd}(r,d)=1$时，$\mathbb{R} \mathbf{M}_{\mathrm{Dol}}(r,d)$的连通分支数与$\mathbb{R} \mathrm{Pic}_d(X)$的相同，这是众所周知的。 显示英文摘要

摘要： Let $X$ be a compact Riemann surface $X$ of genus $\geqslant 2$ and let $\sigma:X \to X$ be an anti-holomorphic involution. Using real and quaternionic systems of Hodge bundles, we study the topology of the real locus $\mathbb{R} \mathbf{M}_{\mathrm{Dol}}(r,d)$ of the moduli space of semistable Higgs bundles of rank $r$ and degree $d$ on $X$, for the induced real structure $(E,\phi) \to (\sigma^*(\overline{E}),\sigma^*(\overline{\phi}))$. We show in particular that, when $\mathrm{gcd}(r,d)=1$, the number of connected components of $\mathbb{R} \mathbf{M}_{\mathrm{Dol}}(r,d)$ coincides with that of $\mathbb{R} \mathrm{Pic}_d(X)$, which is well-known.