Resolution of singularities of pairs preserving semi-simple normal crossings

Details Resolution of singularities of pairs preserving semi-simple normal crossings Resolution of singularities of pairs preserving semi-simple normal crossings

2011-09-14

arxiv.org/abs/1109.3205v1

Mathematics

Algebraic Geometry

41 pages

Scientific paper

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 a point a of X 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 f: X' -> X such that the transformed pair (X',D') 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 Kollar.

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