# Questions tagged [higgs-bundles]

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### Higgs quotient sheaf of a Higgs bundle

Let $X$ be a smooth complex projective variety of dimension $n\geq2$, let $\mathfrak{E}=(E,\varphi)$ be a Higgs bundle over $X$ of rank $r\geq2$.
Does exists a Higgs quotient sheaf $\mathcal{Q}$ of $\...

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### Semistable Higgs bundles and flat connections

Let $\mathfrak{E}=(E,\varphi)$ be a Higgs bundle on a projective manifold $(X,\omega)$ of dimension $n$, where $\omega$ is a Kähler form; the holomorphic structure of $E$ defines an operator $\bar{\...

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### Scheme of Higgs reductions

I'm reading the Bruzzo and Graña Otero's paper Semistable and Numerically Effective Principal (Higgs) Bundles; here: $X$ is a smooth, complex, projective variety; $G$ is a connected, complex, ...