Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Milman, Pierre"'
Publikováno v:
Advances in Mathematics, 385 (2021)
We address the question of whether geometric conditions on the given data can be preserved by a solution in (1) the Whitney extension problem, and (2) the Brenner-Fefferman-Hochster-Koll\'ar problem, both for $\mathcal C^m$ functions. Our results inv
Externí odkaz:
http://arxiv.org/abs/2010.13815
Autor:
Bierstone, Edward, Milman, Pierre D.
Quasianalytic classes are classes of infinitely differentiable functions that satisfy the analytic continuation property enjoyed by analytic functions. Two general examples are quasianalytic Denjoy-Carleman classes (of origin in the analysis of linea
Externí odkaz:
http://arxiv.org/abs/1606.07824
Publikováno v:
In Advances in Mathematics 16 July 2021 385
The main problem studied is resolution of singularities of the cotangent sheaf of a complex- or real-analytic variety Y (or of an algebraic variety Y over a field of characteristic zero). Given Y, we ask whether there is a global resolution of singul
Externí odkaz:
http://arxiv.org/abs/1504.07280
We work with quasianalytic classes of functions. Consider a real-valued function y = f(x) on an open subset U of Euclidean space, which satisfies a quasianalytic equation G(x, y) = 0. We prove that f is arc-quasianalytic (i.e., its restriction to eve
Externí odkaz:
http://arxiv.org/abs/1401.7683
It is shown that, for any reduced algebraic variety in characteristic zero, one can resolve all but simple normal crossings (snc) singularities by a finite sequence of blowings-up with smooth centres which, at every step, avoids points where the tran
Externí odkaz:
http://arxiv.org/abs/1206.5316
Building upon works of Hironaka, Bierstone-Milman, Villamayor and Wlodarczyk, we give an a priori estimate for the complexity of the simplified Hironaka algorithm. As a consequence of this result, we show that there exists canonical Hironaka embedded
Externí odkaz:
http://arxiv.org/abs/1206.3090
Publikováno v:
Advances in Mathematics, 2012, vol. 231, no. 5, pp. 3003-3021
In this sequel to Resolution except for minimal singularities I, we find the smallest class of singularities in four variables with which we necessarily end up if we resolve singularities except for normal crossings. The main new feature is a charact
Externí odkaz:
http://arxiv.org/abs/1107.5598
Autor:
Bierstone, Edward, Milman, Pierre D.
The philosophy of the article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of singularities. The idea is used in two related problems: (1) We give a proof of resolution
Externí odkaz:
http://arxiv.org/abs/1107.5595
We present a constructive criterion for flatness of a morphism of analytic spaces X -> Y or, more generally, for flatness over Y of a coherent sheaf of modules on X. The criterion is a combination of a simple linear-algebra condition "in codimension
Externí odkaz:
http://arxiv.org/abs/1101.1938