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SUMMARY:Moduli spaces of slope-semistable coherent sheaves.  - Matei Toma 
 (Nancy)
DTSTART:20140430T131500Z
DTEND:20140430T141500Z
UID:TALK49263@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:This talk reports on joint work with Daniel Greb.\nLet X be a 
 complex projective manifold\, In order to obtain reasonable moduli spaces 
 for algebraic vector bundles on X\, Mumford introduced the notion of "slop
 e-stability"\nwhen dim(X)=1. His definition was later extended to higher d
 imensions. 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 homeomor
 phic to the compactifications of moduli spaces of Yang-Mills connections o
 btained by Donaldson and Uhlenbeck in gauge theory.\nIn this talk we prese
 nt a construction of a moduli space of slope-semistable coherent sheaves i
 n higher dimensions. We also explain the pathologies connected to change o
 f polarization\, which are encountered in this case. 
LOCATION:MR 13\, CMS
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