Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Bierstone, Edward"'
We address the following question of partial desingularization preserving normal crossings. Given an algebraic (or analytic) variety X in characteristic zero, can we find a finite sequence of blowings-up preserving the normal-crossings locus of X, af
Externí odkaz:
http://arxiv.org/abs/2211.15713
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
If F is an infinitely differentiable function whose composition with a blowing-up belongs to a Denjoy-Carleman class C_M (determined by a log convex sequence M=(M_k)), then F, in general, belongs to a larger shifted class C_N, where N_k = M_2k; i.e.,
Externí odkaz:
http://arxiv.org/abs/2006.10580
We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a polynomially bounded
Externí odkaz:
http://arxiv.org/abs/1907.09502
Publikováno v:
Compositio Math. 154 (2018) 1960-1973
We prove two main results on Denjoy-Carleman classes: (1) a composite function theorem which asserts that a function f(x) in a quasianalytic Denjoy-Carleman class Q, which is formally composite with a generically submersive mapping y=h(x) of class Q,
Externí odkaz:
http://arxiv.org/abs/1709.06629
Autor:
Bierstone, Edward, Parusinski, Adam
Publikováno v:
Duke Math. J. 167, no. 16 (2018), 3115-3128
We give rather simple answers to two long-standing questions in real-analytic geometry, on global smoothing of a subanalytic set, and on transformation of a proper real-analytic mapping to a mapping with equidimensional fibres by global blowings-up o
Externí odkaz:
http://arxiv.org/abs/1705.06331
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
The article develops techniques for solving equations G(x,y)=0, where G(x,y)=G(x_1,...,x_n,y) is a function in a given quasianalytic class (for example, a quasianalytic Denjoy-Carleman class, or the class of infinitely differentiable functions defina
Externí odkaz:
http://arxiv.org/abs/1605.01425
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