Title :

Variations on inversion theorems for Newton–Puiseux series

Author(s) :

García Barroso, Evelia [Auteur]
Universidad de La Laguna [Tenerife - SP] [ULL]
González Pérez, Pedro [Auteur]
Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] [UCM]
Popescu-Pampu, Patrick [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Mathematische Annalen

Pages :

1359-1397

Publisher :

Springer Verlag

Publication date :

2017-08

ISSN :

0025-5831

English keyword(s) :

Branch
Characteristic exponents
plane curve singularities
hypersurface singularities
quasiordinary series
Lagrange inversion
Newton-Puiseux series
. 2010 Mathematics Subject Classification. 14B05 (primary) 14H20 32S25 Branch Characteristic exponents plane curve singularities hypersurface singularities quasiordinary series Lagrange inversion Newton-Puiseux series
. 2010 Mathematics Subject Classification. 14B05 (primary)
14H20
32S25 Branch

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Let f(x, y) be an irreducible formal power series without constant term, over an algebraically closed field of characteristic zero. One may solve the equation f(x, y) = 0 by choosing either x or y as independent variable, ...
Show more >Let f(x, y) be an irreducible formal power series without constant term, over an algebraically closed field of characteristic zero. One may solve the equation f(x, y) = 0 by choosing either x or y as independent variable, getting two finite sets of Newton-Puiseux series. In 1967 and 1968 respectively, Abhyankar and Zariski published proofs of an inversion theorem, expressing the characteristic exponents of one set of series in terms of those of the other set. In fact, a more general theorem, stated by Halphen in 1876 and proved by Stolz in 1879, relates also the coefficients of the characteristic terms of both sets of series. This theorem seems to have been completely forgotten. We give two new proofs of it and we generalize it to a theorem concerning irreducible series with an arbitrary number of variables.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL