arXiv math/05043602005-04-18math.AG

Contraction of excess fibres between the McKay correspondences in dimensions two and three

Samuel Boissiere, Alessandra Sarti

备注：: 21 pages

英文摘要：

The quotient singularities of dimensions two and three obtained from polyhedral groups and the corresponding binary polyhedral groups admit natural resolutions of singularities as Hilbert schemes of regular orbits whose exceptional fibres over the origin reveal similar properties. We construct a morphism between these two resolutions, contracting exactly the excess part of the exceptional fibre. This construction is motivated by the study of some pencils of K3-surfaces arising as minimal resolutions of quotients of nodal surfaces with high symmetries.

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