Weyl Group Covers for Brieskorn’s Resolutions in All Characteristics and the Integral Cohomology of G/P

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