Let $(X,D)$ and $(X^{\prime },D^{\prime })$ be two compact Riemann surfaces of genus $g\ge 4$ with the set of marked points $D\subset X$ and $D^{\prime }\subset X^{\prime }$. Fix a parabolic line bundle L with trivial parabolic structure. Let ${\mathcal{N}}_{\text{Sp}}(2m,\alpha ,L)$ and ${\mathcal{N}}_{\text{Sp}}^{\prime }(2m,\alpha ,L)$ be the moduli spaces of stable symplectic parabolic Higgs bundles over X and $X^{\prime }$ respectively, with rank 2m and fixed parabolic structure α, with the symplectic form taking values in L. We prove that if ${\mathcal{N}}_{\text{Sp}}(2m,\alpha ,L)$ is isomorphic to ${\mathcal{N}}_{\text{Sp}}^{\prime }(2m,\alpha ,L)$, then there exist an isomorphism between X and $X^{\prime }$ sending D to $D^{\prime }$.

中文翻译：

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辛抛物型希格斯束的模空间的Torelli定理

让 $（X，d）$ 和 $（X^{\prime }，d^{\prime }）$ 是两个紧的黎曼曲面 $G\ge 4$ 带有一组标记点 $d\subset X$ 和 $d^{\prime }\subset X^{\prime }$。用平凡的抛物线结构固定抛物线束L。让${\mathcal{ñ}}_{\text{SP}}（\mathrm{2个}米，\alpha ，\mathrm{大号}）$ 和 ${\mathcal{ñ}}_{\text{SP}}^{\prime }（\mathrm{2个}米，\alpha ，\mathrm{大号}）$是稳定的模空间辛抛物线希格斯束在X和$X^{\prime }$分别具有2 m的秩和固定的抛物线结构α，其中辛的形式取L的值。我们证明${\mathcal{ñ}}_{\text{SP}}（\mathrm{2个}米，\alpha ，\mathrm{大号}）$ 同构 ${\mathcal{ñ}}_{\text{SP}}^{\prime }（\mathrm{2个}米，\alpha ，\mathrm{大号}）$，则X和之间存在同构$X^{\prime }$发送D到$d^{\prime }$。