Hostname: page-component-54dcc4c588-trf7k Total loading time: 0 Render date: 2025-10-03T21:14:59.801Z Has data issue: false hasContentIssue false
  • English
  • Français

Derivations and Valuation Rings

Published online by Cambridge University Press:  20 November 2018

P. Fortuny Ayuso
P. Fortuny Ayuso*
Affiliation:
Dpto. de Matemáticas, Universidad de Oviedo, Spain e-mail: info@pfortuny.net
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A complete characterization of valuation rings closed for a holomorphic derivation is given, following an idea of Seidenberg, in dimension 2.

Keywords

32S6513F3013A18singular holomorphic foliationderivationvaluationvaluation ring

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 31 - 38
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Cano, F., Moussu, R., and Rolin, J.-P., Non-oscillating integral curves and valuations. J. Reine Angew. Math. 582 (2005), 107–142. http://dx.doi.org/10.1515/crll.2005.2005.582.107 Google Scholar
[2] Cano, F., Moussu, R., and Sanz, F., Oscillation, spiralement, tourbillonnement. Comment. Math. Helv. 75 (2000), no. 2, 284–318. http://dx.doi.org/10.1007/s000140050127 Google Scholar
[3] Cano, F., Roche, C., and Spivakovsky, M., Local uniformization in characteristic zero. Archimedian case. Rev. Semin. Iberoam. Mat. 3 (2008), no. 5-6, 49–64.Google Scholar
[4] Fortuny Ayuso, P., The valuative theory of foliations, Canad. J. Math. 54 (2002), no. 5, 897–915. http://dx.doi.org/10.4153/CJM-2002-033-x Google Scholar
[5] Seidenberg, A., Reduction of singularities of the differential equation A dy = B dx. Amer. J. Math. 90 (1968), 248–269. http://dx.doi.org/10.2307/2373435 Google Scholar
[6] Seidenberg, A., Derivations and valuation rings. In: Contributions to Algebra. Academic Press, New York, 1977, pp. 343–347.Google Scholar
[7] Spivakovsky, M., Valuations in function fields of surfaces. Amer. J. Math. 112 (1990), no. 1, 107–156. http://dx.doi.org/10.2307/2374856 Google Scholar