An irreducibility criterion for power series
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- by Guillaume Rond and Bernd Schober
- Proc. Amer. Math. Soc. 145 (2017), 4731-4739
- DOI: https://doi.org/10.1090/proc/13635
- Published electronically: June 9, 2017
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Abstract:
We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous results given by García Barroso and González-Pérez.References
- Abdallah Assi, Irreducibility criterion for quasi-ordinary polynomials, J. Singul. 4 (2012), 23–34. MR 2872213, DOI 10.5427/jsing.2012.4b
- E. Artal Bartolo, Pi. Cassou-Noguès, I. Luengo, and A. Melle Hernández, On $\nu$-quasi-ordinary power series: factorization, Newton trees and resultants, Topology of algebraic varieties and singularities, Contemp. Math., vol. 538, Amer. Math. Soc., Providence, RI, 2011, pp. 321–343. MR 2777828, DOI 10.1090/conm/538/10610
- E. Artal Bartolo, Pi. Cassou-Noguès, I. Luengo, and A. Melle Hernández, Quasi-ordinary singularities and Newton trees, Mosc. Math. J. 13 (2013), no. 3, 365–398, 553 (English, with English and Russian summaries). MR 3136099, DOI 10.17323/1609-4514-2013-13-3-365-398
- E. R. García Barroso and P. D. González-Pérez, Decomposition in bunches of the critical locus of a quasi-ordinary map, Compos. Math. 141 (2005), no. 2, 461–486. MR 2134276, DOI 10.1112/S0010437X04001216
- Evelia R. García Barroso and Janusz Gwoździewicz, Quasi-ordinary singularities: tree model, discriminant, and irreducibility, Int. Math. Res. Not. IMRN 14 (2015), 5783–5805. MR 3384457, DOI 10.1093/imrn/rnu106
- Manuel González Villa, Newton process and semigroups of irreducible quasi-ordinary power series, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 108 (2014), no. 1, 259–279. MR 3183117, DOI 10.1007/s13398-013-0139-1
- Heisuke Hironaka, Introduction to the theory of infinitely near singular points, Memorias de Matemática del Instituto “Jorge Juan”, No. 28, Consejo Superior de Investigaciones Científicas, Madrid, 1974. MR 0399505
- A. Grothendieck, J. Dieudonné, Éléments de Géométrie Algébrique IV, Quatrième Partie, Publ. Math. IHÉS, 32, (1967).
- H. Mourtada, B. Schober, A polyhedral characterization of quasi-ordinary singularities, Arxiv:1512.07507.
Bibliographic Information
- Guillaume Rond
- Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
- MR Author ID: 759916
- Email: guillaume.rond@univ-amu.fr
- Bernd Schober
- Affiliation: Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Address at time of publication: The Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada — and — Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, M5S 2E4, Canada
- MR Author ID: 1218416
- ORCID: 0000-0003-0315-0656
- Email: schober@math.toronto.edu
- Received by editor(s): May 19, 2016
- Received by editor(s) in revised form: December 15, 2016
- Published electronically: June 9, 2017
- Additional Notes: The first author was partially supported by ANR projects STAAVF (ANR-2011 BS01 009) and SUSI (ANR-12-JS01-0002-01)
- Communicated by: Irena Peeva
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4731-4739
- MSC (2010): Primary 12E05, 13F25, 14B05, 32S25
- DOI: https://doi.org/10.1090/proc/13635
- MathSciNet review: 3691990