Tony Shaska

Curves of Genus 2 with (N, N) Decomposable Jacobians

Let C be a curve of genus 2 and ?1: C ??E1 a map of degree n, from C to an elliptic curveE1 , both curves defined over C. This map induces a degree n map ?1:P1 ??P1 which we call a Frey?Kani covering. We determine all possible ramifications for ?1. If ?1:C ??E1 is maximal then there exists a maximal map ?2: C ??E2 , of degree n, to some elliptic curveE2 such that there is an isogeny of degree n2from the JacobianJC to E1×E2. We say thatJC is (n, n)-decomposable. If the degree n is odd the pair (?2, E2) is canonically determined. For n= 3, 5, and 7, we give arithmetic examples of curves whose Jacobians are (n, n)-decomposable.

Bielliptic curves of genus 3 in the hyperelliptic moduli

In this paper we study bielliptic curves of genus 3 defined over an algebraically closed field

Genus 3 hyperelliptic curves with (2, 4, 4)-split Jacobians

k

On the field of moduli of superelliptic curves

k and the intersection of the moduli space

A Universal Genus-Two Curve from Siegel Modular Forms

\fancyscript{M}_3^b

On superelliptic curves of level

M3b of such curves with the hyperelliptic moduli