5 problems

Let $\Sigma$ be a smooth surface, let $n$ be a positive integer, and let $\mathcal{T}^n$ denote the moduli space of higher complex structures of order $n$ on $\Sigma$. Let the Hitc…

Let $S$ be a closed oriented surface, let $V$ be the vector bundle constructed from a covector in $T^*\mathcal{T}^n(S)$, and let…

Let $U$ be a neighborhood of the zero-section in T^*\bm\hat{\mathcal{T}}^n, and let $[(\mu_k,t_k)]\in U$. A connection … is considered up to unitary gauge. Local existence and un…

Let $\mu$ and $t$ be the higher-complex-structure data, and consider a connection … Here $\Phi$ is induced by the higher complex structure, and $A$ is the connection term. Uniquene…

Let $\Sigma$ be a closed surface of genus $g\geq 2$, and let $\hat{\mathcal{T}}^n_{\Sigma}$ denote geometric Hitchin space and $\mathcal{T}^n_{\Sigma}$ Hitchin's component. Canonic…