There is an isomorphism between the moduli spaces of $\sigma$-stable holomorphic triples and some of the critical submanifolds of the moduli space of $k$-Higgs bundles of rank three, whose elements $(E,\varphi^k)$ correspond to variations of Hodge structure, VHS. There are special embeddings on the moduli spaces of $k$-Higgs bundles of rank three. The main objective here is to study the cohomology of the critical submanifolds of such moduli spaces, extending those embeddings to moduli spaces of holomorphic triples.

中文翻译：

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三阶k-Higgs丛的hodge结构和全纯三元组的模空间的变化

$\sigma$-稳定全纯三元组的模空间与$k$-三阶希格斯丛的模空间的一些临界子流形之间存在同构，其元素$(E,\varphi^k)$对应于霍奇结构的变体，VHS。在 $k$-Higgs 3 阶包的模空间上有特殊的嵌入。这里的主要目标是研究这种模空间的临界子流形的上同调，将这些嵌入扩展到全纯三元组的模空间。