The minimal model program for orders over surfaces
成果类型：
Article
署名作者：
Chan, D; Ingalls, C
署名单位：
University of New South Wales Sydney; University of New Brunswick
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-005-0438-z
发表日期：
2005
页码：
427-452
关键词：
摘要：
We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique etale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,alpha) consisting of a surface Z and an element alpha of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo.
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