We discuss a generalization of the Kummer construction. Namely an integral representation of a finite group produces an action on an abelian variety and, via a crepant resolution of the quotient, this gives rise to a higher dimensional variety with trivial canonical class and first cohomology. We use virtual Poincar\'e polynomials with coefficients in a ring of representations and McKay correspondence to compute cohomology of such Kummer varieties.
On the Kummer construction
Andreatta, Marco;
2010-01-01
Abstract
We discuss a generalization of the Kummer construction. Namely an integral representation of a finite group produces an action on an abelian variety and, via a crepant resolution of the quotient, this gives rise to a higher dimensional variety with trivial canonical class and first cohomology. We use virtual Poincar\'e polynomials with coefficients in a ring of representations and McKay correspondence to compute cohomology of such Kummer varieties.File in questo prodotto:
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