Displaying similar documents to “Singularity of the moduli space of stable bundles on surfaces”

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.

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.

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...

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.

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...

Symplectic structures on moduli spaces of framed sheaves on surfaces

Francesco Sala (2012)

Open Mathematics

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We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.