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Results tagged with moduli-spaces
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user 146464
Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.
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$\mathbb{C}^*$-action on moduli space of Higgs bundles
Let $M_{r,d}$ be the moduli space of semistable Higgs bundles of rank $r$ and degree $d$ over a compact Riemann surface. Over $M_{r,d}$ we have a $\mathbb{C}^*$-action $$t \cdot (E,\phi)=(E, t \phi). …
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Absolutely indecomposable objects and moduli space
In the setting of moduli spaces of vector bundles/quiver representations etc I've encountered a few times situations like the one that I'll try to explain thereafter .I was wondering if there's a "de …
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Integral locus of Hitchin morphism
Let $\Sigma$ be a Riemann surface of genus $g$. To it, we can associated $M_{Dol}$ be the Higgs moduli space of rank $n$ and degree $d$. Fo simplicity let us take $(n,d)=1$. This quasiprojective varie …
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Non Abelian Hodge theory: underlying structure holomorphic vector bundles
Let $X$ be a compact Riemann surface. We fix a complex vector bundle $E$ of rank $n$ and degree $d$ (unique up to diffeomorphism). From results coming originally (I think at least) by Simpson,Donaldso …
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Quiver varieties associated to D_4
Let $Q=(I,\Omega)$ be the $D_4$ affine quiver. We choose as dimension vector $(2,1,1,1,1)$ (where $2$ is on the central vertex). As this dimension vector is indivisible, we can choose a generic $\the …
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Explicit example de Rham moduli space of connections
Let $\Sigma$ be a Riemann surface and let $n,d$ be two relatively prime integers. We can consider different moduli spaces related to those. On one hand we have:
-$M_{Dol}$ the moduli space of stable …
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Moduli stack of quiver representations
Let $Q$ be a finite quiver. As far as I know there's a great amount of work concerning the so-called quiver varieties one can associate to it. Loosely speaking, these are obtained by taking GIT quotie …
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