### Degenerations of moduli of stable bundles over algebraic curves

Huashi Xia (1995)

Compositio Mathematica

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Huashi Xia (1995)

Compositio Mathematica

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Ancona, Vincenzo, Ottaviani, Giorgio (2001)

Advances in Geometry

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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.

Stephen S. Shatz (1977)

Compositio Mathematica

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Georges Elencwajg, O. Forster (1982)

Annales de l'institut Fourier

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We study holomorphic vector bundles on non-algebraic compact manifolds, especially on tori. We exhibit phenomena which cannot occur in the algebraic case, e.g. the existence of 2-bundles that cannot be obtained as extensions of a sheaf of ideals by a line bundle. We prove some general theorems in deformations theory of bundles, which is our main tool.

Yves Laszlo, Christoph Sorger (1997)

Annales scientifiques de l'École Normale Supérieure

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Wiera Dobrowolska (1993)

Colloquium Mathematicae

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This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on ${\mathbb{P}}^{n}$. Non-negative polynomials in Chern classes are constructed for 4-vector bundles on ${\mathbb{P}}^{4}$ and a generalization of the presented method to r-bundles on ${\mathbb{P}}^{n}$ is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.