Spectral curves, opers and integrable systems

David Ben-Zvi; Edward Frenkel

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Moduli of representations of the fundamental group of a smooth projective variety II

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The geometry of Calogero-Moser systems

Jacques Hurtubise, Thomas Nevins (2005)

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We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the $r$ -th power of the elliptic curve, where $r$ is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties...

Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

Indranil Biswas, Amit Hogadi, Yogish Holla (2014)

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Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.

Spectral curves and integrable systems

Eyal Markman (1994)

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About $G$ -bundles over elliptic curves

Yves Laszlo (1998)

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Let $G$ be a complex algebraic group, simple and simply connected, $T$ a maximal torus and $W$ the Weyl group. One shows that the coarse moduli space $M_{G} (X)$ parametrizing $S$ -equivalence classes of semistable $G$ -bundles over an elliptic curve $X$ is isomorphic to $[Γ (T) \otimes_{Z} X] / W$ . By a result of Looijenga, this shows that $M_{G} (X)$ is a weighted projective space.