4 papers · 1 filter
Thin sets in weighted projective stacks
Stephanie Chan, Daniel Loughran, Nick Rome
We prove an upper bound for the number of rational points of bounded height in a weighted projective stack which lie in a given thin subset. As a consequence, we show that …
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…
Serre's problem for multiple conics
Stephanie Chan, Peter Koymans, Nick Rome
We prove the refined Loughran--Smeets conjecture of Loughran--Rome--Sofos for a wide class of varieties arising as products of conic bundles. One interesting feature of our varieti…
On a conjecture of Wooley and lower bounds for cubic hypersurfaces
V. Vinay Kumaraswamy, Nick Rome
Let be a cubic hypersurface cut out by the vanishing of a non-degenerate rational cubic form in variables. Let denote the num…