On a functional equation arising from hyperbolic geometry.
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Walter Benz (1980)
Aequationes mathematicae
Antonio G. Rodicio (1988)
Manuscripta mathematica
Andrzej Tyc (1979)
Fundamenta Mathematicae
José J. Aparicio, Angel Granja, Tomás Sánchez-Giralda (1999)
Revista Matemática Iberoamericana
The purpose of this paper is to define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers δν = {δν(j)}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties...
Maria Evelina Rossi (1981)
Manuscripta mathematica
C. Rotthaus (1987)
Inventiones mathematicae
S.P. Dutta (1994)
Mathematische Zeitschrift
Craig Huneke (1982)
Mathematische Zeitschrift
A. Simis, J.F. Andrade (1981)
Manuscripta mathematica
Benjamin, E., Bresinsky, H. (2004)
Acta Mathematica Universitatis Comenianae. New Series
Josnei Novacoski, Mark Spivakovsky (2016)
Banach Center Publications
In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects...
Galindo, C. (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
C. Huneke, G. Lyubeznik (1990)
Inventiones mathematicae
Paolo Valabrega (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Veronique Lierde (2011)
Open Mathematics
Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic...
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