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August 2021 Weyl Group Covers for Brieskorn’s Resolutions in All Characteristics and the Integral Cohomology of G/P
N. I. Shepherd-Barron
Michigan Math. J. 70(3): 587-613 (August 2021). DOI: 10.1307/mmj/1593741747

Abstract

Given an affine surface X with rational singularities and minimal resolution X, the covering of the Artin component of the deformation space of X where simultaneous resolutions are achieved is Galois and the Galois group is the Weyl group W associated with the configuration of (2)-curves on X. This gives the existence of actions of W on polynomial rings over Z where the ring of invariants is also polynomial. In turn, this leads to a description of the integral cohomology rings of flag varieties of type ADE that extends the known description of the rational cohomology rings as rings of coinvariants for actions of W.

Citation

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N. I. Shepherd-Barron. "Weyl Group Covers for Brieskorn’s Resolutions in All Characteristics and the Integral Cohomology of G/P." Michigan Math. J. 70 (3) 587 - 613, August 2021. https://doi.org/10.1307/mmj/1593741747

Information

Received: 15 April 2019; Revised: 9 November 2019; Published: August 2021
First available in Project Euclid: 3 July 2020

Digital Object Identifier: 10.1307/mmj/1593741747

Subjects:
Primary: 13A50, 14B07, 14J17, 14M15, 57T15

Rights: Copyright © 2021 The University of Michigan

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Vol.70 • No. 3 • August 2021
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