58 citations · 227 across the 16 of their papers we have counts for
21 papers
Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication
Bogdan Dina, Sorina Ionica, Jeroen Sijsling
We analyze complex multiplication for Jacobians of curves of genus 3, as well as the resulting Shimura class groups and their subgroups corresponding to Galois conjugation over the…
Functionality for isomorphism classes of curves and hypersurfaces
Thomas Bouchet, Reynald Lercier, Jeroen Sijsling +1
We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author…
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…
Cubic function fields with prescribed ramification
Valentijn Karemaker, Sophie Marques, Jeroen Sijsling
This article describes cubic function fields with prescribed ramification, where is a rational function field. We give general equations for such extensions, an explicit…
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…
Canonical models of arithmetic curves
Jeroen Sijsling
In 1983 Takeuchi showed that up to conjugation there are exactly 4 arithmetic subgroups of with signature . Shinichi Mochizuki gave a pur…
Rigorous computation of the endomorphism ring of a Jacobian
Edgar Costa, Nicolas Mascot, Jeroen Sijsling +1
We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.
Plane quartics over with complex multiplication
Pınar Kılıçer, Hugo Labrande, Reynald Lercier +3
We give examples of smooth plane quartics over with complex multiplication over by a maximal order with primitive CM type. We describe the requ…
Reconstructing plane quartics from their invariants
Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling
We present an explicit method that, given a generic tuple of Dixmier-Ohno invariants, reconstructs a corresponding plane quartic curve.
A database of genus 2 curves over the rational numbers
Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland +2
We describe the construction of a database of genus 2 curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated…
On some bounds for symmetric tensor rank of multiplication in finite fields
Stéphane Ballet, Julia Pieltant, Matthieu Rambaud +1
We establish new upper bounds about symmetric bilinear complexity in any extension of finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give examp…
Distributions of traces of Frobenius for smooth plane curves over finite fields
Reynald Lercier, Christophe Ritzenthaler, Florent Rovetta +2
In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperelliptic genus curves over small finite fields. In the present one, we give a heu…
On explicit descent of marked curves and maps
Jeroen Sijsling, John Voight
We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to Dèbes and Emsalem can be used t…
Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields
Reynald Lercier, Christophe Ritzenthaler, Florent Rovetta +1
We study new families of curves that are suitable for efficiently parametrizing their moduli spaces. We explicitly construct such families for smooth plane quartics in order to det…
On computing Belyi maps
Jeroen Sijsling, John Voight
We survey methods to compute three-point branched covers of the projective line, also known as Belyi maps. These methods include a direct approach, involving the solution of a syst…
Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group
Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling
This paper is devoted to the explicit description of the Galois descent obstruction for hyperelliptic curves of arbitrary genus whose reduced automorphism group is cyclic of order…
An explicit expression of the Luroth invariant
Romain Basson, Reynald Lercier, Christophe Ritzenthaler +1
In this short note, we give an algorithm to get an explicit expression of the Luroth invariant in terms of the Dixmier-Ohno invariants. We also get the explicit factorized expressi…