Criteria for Algebraicity of Analytic Functions

View/ Open
Date
2018-11-12MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2018,25Author
Bochnak, Jacek
Gwoździewicz, Janusz
Kucharz, Wojciech
Metadata
Show full item recordOWP-2018-25
Abstract
We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend only on the behavior of such a function along irreducible nonsingular algebraic curves passing trough a given point. In the proofs we use results on algebraicity of formal power series, which are also established in this paper.