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Uniqueness of crepant resolutions and symplectic singularities

Baohua Fu, Yoshinori Namikawa (2004)

Annales de l’institut Fourier

We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4- dimensional symplectic singularities is proved. We also give an example of a symplectic singularity which admits two non-equivalent symplectic resolutions.

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

Indranil Biswas, Amit Hogadi, Yogish Holla (2014)

Open Mathematics

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.

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