Abstract
The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X, D), where D is a divisor on X), we construct a functorial desingularization of all but stable simple normal crossings (stable-snc) singularities, by smooth blowings-up that preserve such singularities. A variety has stable simple normal crossings at a point if, locally, its irreducible components are smooth and transverse in some smooth embedding variety. We also show that our main assertion is false for more general simple normal crossings singularities.
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Research supported in part by NSERC grants OGP0009070 and MRS342058.
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Bierstone, E., Pacheco, F.V. Desingularization preserving stable simple normal crossings. Isr. J. Math. 206, 233–280 (2015). https://doi.org/10.1007/s11856-015-1151-2
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DOI: https://doi.org/10.1007/s11856-015-1151-2