85 citations · 307 across the 23 of their papers we have counts for
24 papers
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…
Explicit computation of symmetric differentials and its application to quasi-hyperbolicity
Nils Bruin, Jordan Thomas, Anthony Várilly-Alvarado
We develop explicit techniques to investigate algebraic quasi-hyperbolicity of singular surfaces through the constraints imposed by symmetric differentials. We apply these methods…
Prym varieties of genus four curves
Nils Bruin, Emre Can Sertöz
Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic…