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

Abstract

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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.

How to cite

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Boissière, 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 -

References

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  14. M. Kapranov, E. Vasserot, Kleinian singularities, derived categories and Hall algebras, Math. Ann. 316 (2000), 565-576 Zbl0997.14001MR1752785
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