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Preprint Number 1580
1580. Raf Cluckers and Omer Friedland and Yosef Yomdin Doubling coverings via resolution of singularities and preparation E-mail: Submission date: 11 March 2019 Abstract: In this paper we provide asymptotic upper bounds on the complexity in two
(closely related) situations. We confirm for the total doubling
coverings and
not only for the chains the expected bounds of the form
κ(U)
≤ K_1(log (1/δ))^{K_2}. This is done in a rather general
setting, i.e. for the δ-complement of a polynomial zero-level
hypersurface Y_0 and for the regular level hypersurfaces Y_c themselves
with no assumptions on the singularities of P. The coefficient K_2
is the
ambient dimension n in the first case and n-1 in the second case.
However,
the question of a uniform behavior of the coefficient K_1 remains open. Mathematics Subject Classification: Keywords and phrases: |
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