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

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 2-3, page 293-302
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topKędzierski, 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 -