Mathematics – Algebraic Geometry
Scientific paper
2009-12-14
Mathematics
Algebraic Geometry
26 pages, any comments are very welcome
Scientific paper
An ordered boundary on a scheme is an ordered set of Cartier divisors. We study various operations on boundaries, including transforms under blow ups. Furthermore, we introduce B-schemes as schemes with boundaries, study their basic properties and interpret them as log-schemes whose stalks of monoids are free. Then we establish functorial desingularization of noetherian quasi-excellent B-schemes of characteristic zero, and deduce functorial embedded desingularization of quasi-excellent schemes of characteristic zero. Finally, a standard simple argument is used to extend these results to other categories, and this includes, in particular, (equivariant) embedded desingularization of the following objects of characteristic zero: qe algebraic stacks, qe schemes, qe formal schemes, complex and non-archimedean analytic spaces.
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