4 papers
Abelian surfaces of small conductor from genus 3 double covers
Raymond van Bommel, Céline Maistret, Jia Shi +1
We describe the construction of a database of roughly half a million abelian surfaces over Q of small conductor arising as Pryms associated to a genus 3 double cover of a genus 1 c…
The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7
Raymond van Bommel, Edgar Costa, Noam D. Elkies +3
We show how Hilbert modular forms can be used in the constructive inverse Galois problem over the rationals. In particular, we prove that the transitive permutation group 17T7, iso…
Computing torsion for plane quartics without using height bounds
Raymond van Bommel
We describe an algorithm that provably computes the rational torsion subgroup of the Jacobian of a curve without relying on height bounds. Instead, the strategy is to find upper bo…
Curve equations from expansions of 1-forms at a nonrational point
Raymond van Bommel, Edgar Costa, Bjorn Poonen +1
We exhibit an algorithm to compute equations of an algebraic curve over a computable characteristic 0 field from the power series expansions of its regular 1-forms at a nonrational…