On Dimension Theorems of the Varieties of Special Divisors on a Curve.
The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain...
We obtain short and unified new proofs of two recent characterizations of hyperellipticity given by Maskit (2000) and Schaller (2000), as well as a way of establishing a relation between them.