6 papers
Gluing curves of genus 1 and 2 along their 2-torsion
Jeroen Hanselman, Sam Schiavone, Jeroen Sijsling
Let (resp. ) be a curve of genus 1 (resp. 2) over a base field whose characteristic does not equal 2. We give criteria for the existence of a curve over whose Ja…
Decomposing Jacobians via Galois covers
Davide Lombardo, Elisa Lorenzo García, Christophe Ritzenthaler +1
Let be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of , up to isogeny, a…
A Prym variety with everywhere good reduction over
Nicolas Mascot, Jeroen Sijsling, John Voight
We compute an equation for a modular abelian surface that has everywhere good reduction over the quadratic field and that does not admit a principal…
Conductor and discriminant of Picard curves
Irene I. Bouw, Angelos Koutsianas, Jeroen Sijsling +1
We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so-called special Picard curves over wit…
Numerical computation of endomorphism rings
Nils Bruin, Jeroen Sijsling, Alexandre Zotine
We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as…
A Database of Belyi Maps
Michael Musty, Sam Schiavone, Jeroen Sijsling +1
We use a numerical method to compute a database of three-point branched covers of the complex projective line of small degree. We report on some interesting features of this data s…