Moduli spaces of slope-semistable coherent sheaves.

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• Matei Toma (Nancy)
• Wednesday 30 April 2014, 14:15-15:15
• MR 13, CMS.

If you have a question about this talk, please contact Dr. J Ross.

This talk reports on joint work with Daniel Greb. Let X be a complex projective manifold, In order to obtain reasonable moduli spaces for algebraic vector bundles on X, Mumford introduced the notion of “slope-stability” when dim(X)=1. His definition was later extended to higher dimensions. For dim(X)>1 Giesecker and Maruyama considered a new stability notion which allowed them to construct also in this case moduli spaces of semistable sheaves. Later Le Potier and Li gave a construction when dim(X)=2 of moduli spaces of slope-semistable sheaves. These spaces are homeomorphic to the compactifications of moduli spaces of Yang-Mills connections obtained by Donaldson and Uhlenbeck in gauge theory. In this talk we present a construction of a moduli space of slope-semistable coherent sheaves in higher dimensions. We also explain the pathologies connected to change of polarization, which are encountered in this case.

This talk is part of the Algebraic Geometry Seminar series.

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