51 citations · 93 across the 9 of their papers we have counts for
11 papers
On the Galois-invariant part of the Weyl group of the Picard lattice of a K3 surface
Wim Nijgh, Ronald van Luijk
Let denote a K3 surface over an arbitrary field . Let denote a separable closure of and let denote the base change of to . The…
Concurrent lines on del Pezzo surfaces of degree one
Ronald van Luijk, Rosa Winter
Let be a del Pezzo surface of degree one over an algebraically closed field , and let be its canonical divisor. The morphism induced by the linear system …
The action of the Weyl group on the root system
Rosa Winter, Ronald van Luijk
Let be the graph on the roots of the root system, where any two distinct vertices and are connected by an edge with color equal to the inner product of and $f…
Unirationality of del Pezzo surfaces of degree two over finite fields
Dino Festi, Ronald van Luijk
We prove that every del Pezzo surface of degree two over a finite field is unirational, building on the work of Manin and an extension by Salgado, Testa, and Várilly-Alvarado, who…
Unirationality of del Pezzo surfaces of degree two over finite fields (extended version)
Dino Festi, Ronald van Luijk
We prove that every del Pezzo surface of degree two over a finite field is unirational, building on the work of Manin and an extension by Salgado, Testa, and Várilly-Alvarado, who…
Density of rational points on del Pezzo surfaces of degree one
Cecilia Salgado, Ronald van Luijk
We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski den…
Computing Néron-Severi groups and cycle class groups
Bjorn Poonen, Damiano Testa, Ronald van Luijk
Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron-Severi group of any smooth projective…
Explicit Selmer groups for cyclic covers of P^1
Michael Stoll, Ronald van Luijk
For any abelian variety J over a global field k and an isogeny phi: J -> J, the Selmer group Sel^phi(J,k) is a subgroup of the Galois cohomology group H^1(Gal(ksep/k), J[phi]), def…
Density of rational points on elliptic surfaces
Ronald van Luijk
Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V, not eq…
Two-coverings of Jacobians of curves of genus two
E. Victor Flynn, Damiano Testa, Ronald van Luijk
We find explicit equations for two-coverings of Jacobians of genus two curves over an arbitrary ground field of characteristic different from two.
On Character varieties of two-bridge knot groups
Melissa L. Macasieb, Kathleen L. Petersen, Ronald M. van Luijk
We find explicit models for the PSL(2,C)- and SL(2,C)-character varieties of the fundamental groups of complements in S^3 of an infinite family of two-bridge knots that contains th…