Constructs a series of Nash blowups of singular foliations that turn any such foliation into a Debord foliation after one step, recovering prior cases for i=0 and i=1.
Blowups and Resolution
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abstract
This article shall serve as a quick reference for somebody who needs precise information on concepts and results related to resolution of singularities. As such, it is more a technical manual than a bedtime story. Topics which are covered: Singular and regular points of varieties and schemes; various definitions of blowups and their mutual relations; properties of blowups; transforms of varieties, schemes and ideals; exceptional divisors; Cartier and normal crossings divisors; transversality; hypersurfaces of maximal contact; flags; coefficient ideals; resolution invariants; order of ideals; Hilbert-Samuel function; semicontinuity; various resolution statements; characteristic zero resolution; characteristic p phenomena. The text is complemented with lots of illustrating examples.
fields
math.DG 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
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A series of Nash resolutions of a singular foliation
Constructs a series of Nash blowups of singular foliations that turn any such foliation into a Debord foliation after one step, recovering prior cases for i=0 and i=1.