Towards the multiplicative behavior of the K-theoretical McKay correspondence

Details Towards the multiplicative behavior of the K-theoretical McKay correspondence Towards the multiplicative behavior of the K-theoretical McKay correspondence

2005-01-24

arxiv.org/abs/math/0501407v2

Mathematics

Algebraic Geometry

19 pages; to appear in Mathematische Zeitschrift

Scientific paper

When the quotient of a symplectic vector space by the action of a finite subgroup of symplectic automorphisms admits as a crepant projective resolution of singularities the Hilbert scheme of regular orbits of Nakamura, then there is a natural isomorphism between the Grothendieck group of this resolution and the representation ring of the group, given by the Bridgeland-King-Reid map. However, this isomorphism is not compatible with the ring structures. For the Hilbert scheme of points on the affine plane, we study the multiplicative behavior of this map.

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