On generalized Fermat curves: their automorphisms and fields of definition |
| Saúl Quispe |
| Universidad de La Frontera |
| Abstract |
| A closed Riemann surface \(S\) which admits a group \(H\cong C_k^n\) of conformal automorphisms such that \(S/H\) has genus zero with exactly \((n+1)\) cone points, each one of order \(k\), where \(k, n\geq 2\) are integers such that \((k − 1)(n − 1)>2\), is called a hyperbolic generalized Fermat curve of type \((k, n)\). In this talk we discuss some results concerning their groups of automorphism, and we provide conditions for the field of moduli to be a field of definition. |
| Joint work with Rubén A. Hidalgo and Yasmina Atarihuna. |
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