3 citations · 6 across the 8 of their papers we have counts for
9 papers
Counting quadratic points on Fano varieties
Francesca Balestrieri, Kevin Destagnol, Julian Lyczak +2
This paper initiates the systematic study of the number of points of bounded height on symmetric squares of weak Fano varieties. We provide a general framework for establishing the…
Local solubility in generalised Châtelet varieties
Kevin Destagnol, Julian Lyczak, Efthymios Sofos
We obtain asymptotic formulas for averages of general multivariate arithmetic functions evaluated at polynomial arguments using recent work of Rydin Myerson and Rome-Yamagishi. We…
Cubic surfaces failing the integral Hasse principle
Julian Lyczak, Vladimir Mitankin, H. Uppal
We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this s…
Paucity of rational points on fibrations with multiple fibres
Tim Browning, Julian Lyczak, Arne Smeets
Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allo…
Local solubility for a family of quadrics over a split quadric surface
Tim Browning, Julian Lyczak, Roman Sarapin
We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface.
Quartic del Pezzo surfaces with a Brauer group of order 4
Julian Lyczak, Roman Sarapin
We study arithmetic properties of del Pezzo surfaces of degree 4 for which the Brauer group has the largest possible order using different fibrations into curves. We show that if s…
The Batyrev-Tschinkel conjecture for a non-normal cubic surface and its symmetric square
Nils Gubela, Julian Lyczak
We complete the study of points of bounded height on irreducible non-normal cubic surfaces by doing the point count on the cubic surface given by over a…
Order 5 Brauer-Manin obstructions to the integral Hasse principle on log K3 surfaces
Julian Lyczak
We construct families of log K3 surfaces and study the arithmetic of their members. We use this to produce explicit surfaces with an order 5 Brauer-Manin obstruction to the integra…
A uniform bound on the Brauer groups of certain log K3 surfaces
Martin Bright, Julian Lyczak
Let U be the complement of a smooth anticanonical divisor in a del Pezzo surface of degree at most 7 over a number field k. We show that there is an effective uniform bound for the…