Displaying similar documents to “The cohomology rings of moduli stacks of principal bundles over curves.”

Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Constantin Teleman, Christopher Woodward (2003)

Annales de l’institut Fourier

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The set of conjugacy classes appearing in a product of conjugacy classes in a compact, 1 -connected Lie group K can be identified with a convex polytope in the Weyl alcove. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety G / P , where G is the complexification of K and P is a maximal parabolic subgroup. This generalizes the results for S U ( n ) of Agnihotri and the second author...

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

Indranil Biswas, Amit Hogadi, Yogish Holla (2014)

Open Mathematics

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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.

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.

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...

SUX(r, L) is separably unirational

Georg Hein (2009)

Open Mathematics

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We show that the moduli space of SUX (r, L) of rank r bundles of fixed determinant L on a smooth projective curve X is separably unirational.

Bubble tree compactification of moduli spaces of vector bundles on surfaces

Dimitri Markushevich, Alexander Tikhomirov, Günther Trautmann (2012)

Open Mathematics

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We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c...

Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.

Indranil Biswas (2003)

Collectanea Mathematica

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Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights...