19 citations · 22 across the 9 of their papers we have counts for
9 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…
Reduction of Plane Quartics and Dixmier-Ohno invariants
Raymond van Bommel, Jordan Docking, Reynald Lercier +1
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determini…
Reduction of Plane Quartics and Cayley Octads
Raymond van Bommel, Jordan Docking, Vladimir Dokchitser +2
We give a conjectural characterisation of the stable reduction of plane quartics over local fields in terms of their Cayley octads. This results in p-adic criteria that efficiently…
Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
Raymond van Bommel, Shiva Chidambaram, Edgar Costa +1
We describe an efficient algorithm which, given a principally polarized (p.p.) abelian surface over with geometric endomorphism ring equal to , compute…
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…
Efficient computation of BSD invariants in genus 2
Raymond van Bommel
Recently, all Birch and Swinnerton-Dyer invariants, except for the order of Sha, have been computed for all curves of genus 2 contained in the L-functions and Modular Forms Databas…
Boundedness in families with applications to arithmetic hyperbolicity
Raymond van Bommel, Ariyan Javanpeykar, Ljudmila Kamenova
Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to…
Numerical verification of the Birch and Swinnerton-Dyer conjecture for hyperelliptic curves of higher genus over up to squares
Raymond van Bommel
The Birch and Swinnerton-Dyer conjecture has been numerically verified for the Jacobians of 32 modular hyperelliptic curves of genus 2 by Flynn, Leprévost, Schaefer, Stein, Stoll a…