Displaying similar documents to “On the polynomial-like behaviour of certain algebraic functions”

On the space of morphisms into generic real algebraic varieties

Riccardo Ghiloni (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let Z be a real algebraic variety. We say that Z is generic if there exist a finite family { D i } i = 1 n of irreducible real algebraic curves with genus ≥ 2 and a biregular embedding of Z into the product variety ∏ i = 1 n D i . A bijective map ϕ : Z ˜ 1 → Z from a real algebraic variety Z ˜ to Z is called weak change of the algebraic structure of  Z if it is regular and its inverse is a Nash map. Generic real algebraic...

On algebraic solutions of algebraic Pfaff equations

Henryk Żołądek (1995)

Studia Mathematica

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We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system ẋ = z s , ẏ = x s , ż = y s . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.