Questions tagged [higgs-bundles]

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Has anyone studied the derived category of Higgs sheaves?

Let $X$ be a complex manifold and $\Omega^1_X$ be the sheaf of holomorphic $1$-forms on $X$. A Higgs bundle on $X$ is a holomorphic vector bundle $E$ together with a morphism of $\mathcal{O}_X$-...
Zhaoting Wei's user avatar
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Simpson correspondence for perverse sheaves

Let $X$ be a projective complex manifold. Then Simpson's correspondence from nonabelian Hodge theory shows that the category of semisimple local systems on $X$ is equivalent to the category of ...
Doug Liu's user avatar
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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, ...
Armando j18eos's user avatar
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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 $\...
Armando j18eos's user avatar
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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{\...
Armando j18eos's user avatar
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Is this a correct description of the BPS monopole of charge $1$?

I am reading the book "The Geometry and Dynamics of Magnetic Monopoles", by M.F. Atiyah and N.J. Hitchin, and I got to this part: "... let $H$ be the Hopf line bundle over $S^2$ and ...
Malkoun's user avatar
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Invariance of numerical class of a curve in Higgs-Grassmann schemes

Premise Let $X$ be a projective variety of dimension $n\geq1$ over an algebraically closed field of characteristic $0$. A Higgs sheaf $\mathfrak{E}$ is a pair $(E,\varphi)$ where $E$ is a $\mathcal{...
Armando j18eos's user avatar