2010 / December Volume 5 No.4
On hyperellipticity degree of bisymmetric Riemann surfaces admitting a fixed point free symmetry
| Published Date |
2010 / December
|
|---|---|
| Title | On hyperellipticity degree of bisymmetric Riemann surfaces admitting a fixed point free symmetry |
| Author | |
| Keyword | |
| Download | |
| Pagination | 457-468 |
| Abstract | We study pairs of commuting
symmetries of a Riemann surface of genus $g\geq 2$,
assuming that one of them is fixed point free. We find necessary and sufficient conditions
for an integer $p$ to be the degree of hyperellipticity of their
product, being given the number of ovals and separabilities of the
symmetries. In the last part of the paper, using well known formula
on the number $m$ of points fixed by the conformal involution of a
Riemann surface, we find all possible values of $m$ that can be
attained for the product of our symmetries.
|
| AMS Subject Classification |
30F50, 14H37
|
| Received |
2010-03-09
|
| Accepted |
2010-03-12
|