Mathematics and Statistics Faculty Scholarship

Permanent URI for this collection

Now showing 1 - 2 of 2

Cyclic curves over the reals
(eprint arXiv:1501.01559, 2014-11-15) Izquierdo, Milagros; Shaska, Tony
In this paper we study the automorphism groups of real curves admitting a regular meromorphic function f of degree p, so called real cyclic p-gonal curves. When p = 2 the automorphism groups of real hyperelliptic curves where given by Bujalance et al. in [4].
Thetanulls of cyclic curves of small genus
(Albanian J. Math., 2007-12-15) Previato, Emma; Shaska, Tony; Wijesiri, Sujeeva
We study relations among the classical thetanulls of cyclic curves, namely curves $\X$ (of genus $g(\X )>1$ ) with an automorphism $\s$ such that $\s$ generates a normal subgroup of the group $G$ of automorphisms, and $g \left( \X/ \<\s\> \right) =0$. Relations between thetanulls and branch points of the projection are the object of much classical work, especially for hyperelliptic curves, and of recent work, in the cyclic case. We determine the curves of genus 2 and 3 in the locus $\mathcal M_g (G, \textbf{C})$ for all $G$ that have a normal subgroup $\langle\s\rangle$ as above, and all possible signatures \textbf{C}, via relations among their thetanulls.