85 citations · 307 across the 23 of their papers we have counts for
22 papers · 1 filter
Explicit Brauer-Manin obstructions on plane quartics
Nils Bruin, Brendan Creutz
We describe a method to show a plane quartic over a number field has no rational points. The method can be adapted to show that a curve does not have divisors of degree 1 or 2 and…
Twists of the Burkhardt Quartic Threefold
Nils Bruin, Eugene Filatov
We study twists of the Burkhardt quartic threefold over non-algebraically closed base fields of characteristic different from 2,3,5. We show they all admit quartic models in projec…
Genus two curves with full -level structure and Tate-Shafarevich groups
Nils Bruin, E. Victor Flynn, Ari Shnidman
We give an explicit rational parameterization of the surface over whose points parameterize genus 2 curves~ with full -level structure on…
Two-cover descent on plane quartics with rational bitangents
Nils Bruin, Daniel Lewis
We implement two-cover descent for plane quartics over Q with all 28 bitangents rational and show that on a significant collection of test cases, it resolves the existence of ratio…
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…
Arithmetic aspects of the Burkhardt quartic threefold
Nils Bruin, Brett Nasserden
We show that the Burkhardt quartic threefold is rational over any field of characteristic distinct from 3. We compute its zeta function over finite fields. We realize one of its mo…