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Stacky Resolutions of Singular Schemes

Matthew Satriano

出版	University of California, Berkeley, 2010
URL	http://books.google.com.hk/books?id=B72fAQAACAAJ&hl=&source=gbs_api

註釋

Given a singular scheme X over a field k, we consider the problem of resolving the singularities of X by an algebraic stack. When X is a toroidal embedding or is etale locally the quotient of a smooth scheme by a linearly reductive group scheme, we show that such "stacky resolutions" exist. Moreover, these resolutions are canonical and easily understandable in terms of the singularities of X. We give three applications of our stacky resolution theorems: various generalizations of the Chevalley-Shephard-Todd Theorem, a Hodge decomposition in characteristic p, and a theory of toric Artin stacks extending the work of Borisov-Chen-Smith. While these applications are seemingly different, they are all related by the common theme of using stacky resolutions to study singular schemes.