Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant

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dc.creatorBierstone, Edward
dc.creatorMilman, Pierre
dc.date1995-08-15
dc.date1995-08-16
dc.date.accessioned2026-07-07T08:58:00Z
dc.date.available2026-07-07T08:58:00Z
dc.descriptionThis article contains an elementary constructive proof of resolution of singularities in characteristic zero. Our proof applies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka). We introduce a discrete local invariant $\inv_X (a)$ whose maximum locus determines a smooth centre of blowing up, leading to desingularization. To define $\inv_X$, we need only to work with a category of local-ringed spaces $X=(|X|,{\cal O}_X)$ satisfying certain natural conditions. If $a\in |X|$, then $\inv_X(a)$ depends only on $\widehat{\cal O}_{X,a}$. More generally, $\inv_X(a)$ is defined inductively after any sequence of blowings-up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of $\inv_X(\cdot)$. The paper is self-contained and includes detailed examples. One of our goals is that the reader understand the desingularization theorem, rather than simply ``know'' it is true.
dc.descriptionPS, Only the first chapter is available from Algebraic- Geometry E-prints. A complete manuscript (86 pages, approx. 340K) is available on WWW as a gzipped DVI file in binary mode at ftp://wave.scar.utoronto.ca/pub/math-preprints/bierstone/desingular.dvi.gz A hard copy is also available on request
dc.identifierhttps://arxiv.org/abs/alg-geom/9508005
dc.identifierhttp://arxiv.org/abs/alg-geom/9508005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147154
dc.subjectAlgebraic Geometry
dc.titleCanonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
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