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Towards the multiplicative behavior of the K-theoretical McKay correspondence

Samuel Boissiere
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Abstract

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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Samuel Boissiere. 2005-05-01. Towards the multiplicative behavior of the K-theoretical McKay correspondence. https://arxiv.org/abs/math/0501407

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