5 citations · 15 across the 11 of their papers we have counts for
12 papers
Finiteness theorems for K3 surfaces over arbitrary fields
Martin Bright, Adam Logan, Ronald van Luijk
Over an algebraically closed field, various finiteness results are known regarding the automorphism group of a K3 surface and the action of the automorphisms on the Picard lattice.…
The Cayley-Oguiso automorphism of positive entropy on a K3 surface
Dino Festi, Alice Garbagnati, Bert van Geemen +1
Recently Oguiso showed the existence of K3 surfaces that admit a fixed point free automorphism of positive entropy. The K3 surfaces used by Oguiso have a particular rank two Picard…
Density of rational points on diagonal quartic surfaces
Adam Logan, David McKinnon, Ronald van Luijk
Let a,b,c,d be nonzero rational numbers whose product is a square, and let V be the diagonal quartic surface in PP^3 defined by ax^4+by^4+cz^4+dw^4=0. We prove that if V contains a…
Lines on Fermat surfaces
Matthias Schuett, Tetsuji Shioda, Ronald van Luijk
We prove that the Neron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relati…
Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces
Ronald van Luijk
We show that if over some number field there exists a certain diagonal plane cubic curve that is locally solvable everywhere, but that does not have points over any cubic galois ex…
Nontrivial elements of Sha explained through K3 surfaces
Adam Logan, Ronald van Luijk
In this paper we present a new method to show that a principal homogeneous space of the Jacobian of a curve of genus two is nontrivial. The idea is to exhibit a Brauer-Manin obstru…