Articulo
On the field of moduli of superelliptic curves
Contemporary Mathematics
Registro en:
1150003
1150003
Autor
Hidalgo-Ortega, Rubén Antonio
Shaska, Tony
Institución
Resumen
A superelliptic curve chi of genus g >= 2 is not necessarily defined over its field of moduli but it can be defined over a quadratic extension of it. While a lot of work has been done by many authors to determine which hyperelliptic curves are defined over their field of moduli, less is known for superelliptic curves. In this paper we observe that if the reduced group of a genus g >= 2 superelliptic curve chi is different from the trivial or cyclic group, then chi can be defined over its field of moduli in the cyclic situation we provide a sufficient condition for this to happen. We also determine those families of superelliptic curves of genus at most 10 which might not be definable over their field of moduli. Regular 2015 FONDECYT FONDECYT