Resolution of singularities of pairs preserving semi-simple normal crossings

Let X denote a reduced algebraic variety and D a Weil divisor on X . The pair ( X , D ) is said to be semi-simple normal crossings (semi-snc) at if X is simple normal crossings at a (i.e., a simple normal crossings hypersurface, with respect to a local embedding in a smooth ambient variety), and D i...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2013-03, Vol.107 (1), p.159-188
Main Authors: Bierstone, Edward, Vera Pacheco, Franklin
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
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Summary:Let X denote a reduced algebraic variety and D a Weil divisor on X . The pair ( X , D ) is said to be semi-simple normal crossings (semi-snc) at if X is simple normal crossings at a (i.e., a simple normal crossings hypersurface, with respect to a local embedding in a smooth ambient variety), and D is induced by the restriction to X of a hypersurface that is simple normal crossings with respect to X . We construct a composition of blowings-up such that the transformed pair is everywhere semi-simple normal crossings, and f is an isomorphism over the semi-simple normal crossings locus of ( X , D ). The result answers a question of Kollár.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-012-0092-4