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

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

2005-04-18

arxiv.org/abs/math/0504360v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

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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