On Fields of Definition of an Algebraic Curve

On Fields of Definition of an Algebraic Curve

The paper deals with geometric invariants of an algebraic curve such as the minimal number of crucial values of rational functions and the minimal transcendence degree of definition fields. The main question is if the difference of these two invariants is always equal to 3 for any curve with genus g...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2016-12, Vol.219 (3), p.484-491
1. Verfasser: Smirnov, A. L.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Invariants
Mathematics
Mathematics and Statistics
Rational functions
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The paper deals with geometric invariants of an algebraic curve such as the minimal number of crucial values of rational functions and the minimal transcendence degree of definition fields. The main question is if the difference of these two invariants is always equal to 3 for any curve with genus g > 0. For curves defined over an algebraic number field, a positive answer is given by Belyi’s theorem. In the paper, the main question is answered in the affirmative for some other cases.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-016-3121-6