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Abstract des Vortrages von Norbert Hoffmann

Essential Dimension of Vector Bundles

 

The essential dimension of an algebro-geometric object has been defined by Buhler-Reichstein and Merkurjev. It measures the number of algebraically independent parameters necessary to define the object. In the case of algebraic vector bundles, this turns out to involve the number of moduli and the difference between fields of moduli and fields of definition. In line with the genericity principle due to Brosnan, Reichstein and Vistoli, the largest essential dimension among vector bundles of fixed rank and degree over a fixed curve is usually that of a generic bundle. But there are exceptions if the curve is elliptic.