## 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.

Original language | English |
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Pages (from-to) | 587-613 |

Number of pages | 27 |

Journal | Michigan Mathematical Journal |

Volume | 70 |

Issue number | 3 |

Early online date | 3 Jul 2020 |

DOIs | |

Publication status | Published - Aug 2021 |

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