Constructiveness of Hironaka's resolution
A new proof of desingularization over fields of characteristic zero.
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This is done by showing that desingularization...
An extension to fields of positive characteristic of Mather's construction of the Thom-Boardman sequence
A simplified proof of desingularization and applications.
This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of desingularization of families of embedded schemes, and a formulation of desingularization which is stronger than Hironaka's). Our proof avoids the use of the Hilbert-Samuel function and Hironaka's notion of normal flatness: First we define a procedure for principalization of...
An algebraic construction of the generic singularities of Boardman-Thom
Sur les algèbres de Clifford
Algèbres de Clifford et groupe de Brauer
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