TY - JOUR
T1 - Weyl group covers for Brieskorn's resolutions in all characteristics and the integral cohomology of G/P
AU - Shepherd-Barron, N. I.
PY - 2021/8
Y1 - 2021/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85113934296&partnerID=8YFLogxK
U2 - 10.1307/mmj/1593741747
DO - 10.1307/mmj/1593741747
M3 - Article
SN - 0026-2285
VL - 70
SP - 587
EP - 613
JO - Michigan Mathematical Journal
JF - Michigan Mathematical Journal
IS - 3
ER -