Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)

Kędzierski, Oskar. "Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)." Serdica Mathematical Journal 30.2-3 (2004): 293-302. <http://eudml.org/doc/219545>.

@article{Kędzierski2004,
abstract = {2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic group not in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to the integral cohomology on the resolution.},
author = {Kędzierski, Oskar},
journal = {Serdica Mathematical Journal},
keywords = {McKay Correspondence; Resolutions of Terminal Quotient Singularities; G-Hilbert Scheme; McKay correspondence; terminal singularities},
language = {eng},
number = {2-3},
pages = {293-302},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)},
url = {http://eudml.org/doc/219545},
volume = {30},
year = {2004},
}

TY - JOUR
AU - Kędzierski, Oskar
TI - Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)
JO - Serdica Mathematical Journal
PY - 2004
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 30
IS - 2-3
SP - 293
EP - 302
AB - 2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic group not in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to the integral cohomology on the resolution.
LA - eng
KW - McKay Correspondence; Resolutions of Terminal Quotient Singularities; G-Hilbert Scheme; McKay correspondence; terminal singularities
UR - http://eudml.org/doc/219545
ER -