Displaying similar documents to “Integrable systems and moduli spaces of rank two vector bundles on a non-hyperelliptic genus 3 curve”

Moduli Spaces of PU ( 2 ) -Instantons on Minimal Class VII Surfaces with b 2 = 1

Konrad Schöbel (2008)

Annales de l’institut Fourier

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We describe explicitly the moduli spaces ℳ g pst ( S , E ) of polystable holomorphic structures ℰ with det ℰ ≅ 𝒦 on a rank two vector bundle E with c 1 ( E ) = c 1 ( K ) and c 2 ( E ) = 0 for all minimal class VII surfaces S with b 2 ( S ) = 1 and with respect to all possible Gauduchon metrics g . These surfaces S are non-elliptic and non-Kähler complex surfaces and have recently been completely classified. When S is a half or parabolic Inoue surface, ℳ g pst ( S , E ) is always a compact one-dimensional complex disc. When S is an Enoki surface, one obtains a complex...

On the motives of moduli of chains and Higgs bundles

Oscar García-Prada, Jochen Heinloth, Alexander Schmitt (2014)

Journal of the European Mathematical Society

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We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the n -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space...

A Torelli theorem for moduli spaces of principal bundles over a curve

Indranil Biswas, Norbert Hoffmann (2012)

Annales de l’institut Fourier

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Let X and X ′ be compact Riemann surfaces of genus ≥ 3 , and let G and G ′ be nonabelian reductive complex groups. If one component ℳ G d ( X ) of the coarse moduli space for semistable principal G –bundles over X is isomorphic to another component ℳ G ′ d ′ ( X ′ ) , then X is isomorphic to X ′ .

The Picard group of a coarse moduli space of vector bundles in positive characteristic

Norbert Hoffmann (2012)

Open Mathematics

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Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,Lss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,Lss) = ℤ, identify the ample generator, and deduce that M r,Lss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric...

The Brauer group of desingularization of moduli spaces of vector bundles over a curve

Indranil Biswas, Amit Hogadi, Yogish Holla (2012)

Open Mathematics

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Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.