WorldCat Identities

Cossart, Vincent 1950-

Overview
Works: 6 works in 24 publications in 3 languages and 470 library holdings
Classifications: QA571, 516.35
Publication Timeline
Key
Publications about  Vincent Cossart Publications about Vincent Cossart
Publications by  Vincent Cossart Publications by Vincent Cossart
Most widely held works by Vincent Cossart
Resolution of surface singularities : three lectures by Vincent Cossart ( Book )
19 editions published in 1984 in English and German and held by 442 WorldCat member libraries worldwide
Resolution of Surface Singularities Three Lectures with an Appendix by H. Hironaka by Vincent Cossart ( )
1 edition published in 1984 in English and held by 22 WorldCat member libraries worldwide
Polyèdre caractéristique d'une singularité by Vincent Cossart ( Book )
1 edition published in 1987 in French and held by 3 WorldCat member libraries worldwide
CETTE THESE EST CONSACREE A L'ETUDE DES DESINGULARISATIONS EN CARACTERISTIQUE POSITIVE A L'AIDE POLYEDRE CARACTERISTIQUE DE LA SINGULARITE. DANS LA PARTIE PRINCIPALE, NOUS RESOLVONS LA SINGULARITE D'UN REVETEMENT PUREMENT INSEPARABLE D'UN ESPACE LISSE DE DIMENSION TROIS. LES DEUX AUTRES PARTIES SONT CONSACREES A LA DESINGULARISATION DES SURFACES EN CARACTERISTIQUE POSITIVE
Polyèdre caractéristique d'une singularité by Vincent Cossart ( Book )
1 edition published in 1987 in French and held by 1 WorldCat member library worldwide
Resolution of Surface Singularites : Three Lectures with an Appendix by H. Hironaka, Edited by U. Orbanz ( Book )
1 edition published in 1984 in Undetermined and held by 1 WorldCat member library worldwide
L'uniformisation locale des surfaces d'Artin-Schreier en caractéristique positive by Raphaël Astier ( Book )
1 edition published in 2002 in French and held by 1 WorldCat member library worldwide
This thesis deals with uniformization, in characteristic p>0, of a rational valuation, in special cases where this valuation is centered on a singularity locally defined by the following equations :- either zp̂+f(x,y)=0, with f not a p-th power, and ordf >p,- or zp̂+e(x,y)z+f(x,y)=0, with ord (ez+f)>p (Artin-Schreier's case).Historically, it was in such cases that all difficulty of resolving surfaces in positive characteristic was concentrated.The novelty bringed in this work consists first in giving a bound to theminimum number of closed point's blowing-ups needed to uniformize, and second in anticipating (from the first ring) the Newton polygon's evolution and the parameter's choice for the successive blowing-ups along the valuation. In a first part, we come back on the Giraud's normal form of f in O_X(X)where X is a two dimensional regular scheme of characteristic p. The startingpoint is an polynomial expansion of f with a generating sequence for the valuation. We can then study and anticipate the behavior of this expansion and the associated Newton polygon modulo a p-th power. We then give a bound on the maximum number of blowing-ups needed for this polygon to become minimal, with only one vertex, and of maximal height one. This case correspond to the normal form of f.In a second part, using this results for the two above-mentionned cases, wegive an algorithm witch anticipate, in the first ring, the translations on zneeded to keep a minimal Newton polygon during the blowing-ups sequence (alongthe valuation), and we quantify the maximal size of such a sequence with last ring corresponding to a quasi-ordinary singularity
 
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.79 (from 0.00 for Polyèdre ... to 0.81 for Resolution ...)
Languages
English (19)
French (3)
German (1)
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