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

Samuel Boissière^{[1]}; Alessandra Sarti^{[2]}

- [1] Université de Nice Sophia-Antipolis Laboratoire J.A.Dieudonné UMR CNRS 6621 Parc Valrose 06108 Nice (France)
- [2] Johannes Gutenberg Universität Mainz Institut für Mathematik 55099 Mainz (Deutschland)

Annales de l’institut Fourier (2007)

- Volume: 57, Issue: 6, page 1839-1861
- ISSN: 0373-0956

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topBoissière, Samuel, and Sarti, Alessandra. "Contraction of excess fibres between the McKay correspondences in dimensions two and three." Annales de l’institut Fourier 57.6 (2007): 1839-1861. <http://eudml.org/doc/10279>.

@article{Boissière2007,

abstract = {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 appearing as minimal resolutions of quotients of nodal surfaces with high symmetries.},

affiliation = {Université de Nice Sophia-Antipolis Laboratoire J.A.Dieudonné UMR CNRS 6621 Parc Valrose 06108 Nice (France); Johannes Gutenberg Universität Mainz Institut für Mathematik 55099 Mainz (Deutschland)},

author = {Boissière, Samuel, Sarti, Alessandra},

journal = {Annales de l’institut Fourier},

keywords = {Quotient singularities; McKay correspondence; Hilbert schemes; polyhedral groups; quotient singularities},

language = {eng},

number = {6},

pages = {1839-1861},

publisher = {Association des Annales de l’institut Fourier},

title = {Contraction of excess fibres between the McKay correspondences in dimensions two and three},

url = {http://eudml.org/doc/10279},

volume = {57},

year = {2007},

}

TY - JOUR

AU - Boissière, Samuel

AU - Sarti, Alessandra

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

JO - Annales de l’institut Fourier

PY - 2007

PB - Association des Annales de l’institut Fourier

VL - 57

IS - 6

SP - 1839

EP - 1861

AB - 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 appearing as minimal resolutions of quotients of nodal surfaces with high symmetries.

LA - eng

KW - Quotient singularities; McKay correspondence; Hilbert schemes; polyhedral groups; quotient singularities

UR - http://eudml.org/doc/10279

ER -

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