Hyperbola method and Campana points on toric varieties

Marta Pieropan (Utrecht U)

Sep 23. 2021, 11:00 — 12:00

In joint work with Damaris Schindler we develop a new version of the hyperbola method for counting rational points of bounded height that generalizes the work of Blomer and Brüdern for products of projective spaces. The hyperbola method tranforms a counting problem into an optimization problem on certain polytopes. For rational points on toric varieties the polytopes have a geometric meaning that reflects Manin's conjecture, and the same holds for counts of Campana points of bounded height. I will present our results as well as some general heuristics.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Arithmetic Statistics and Local-Global Principles (Workshop)
Tim Browning (ISTA, Klosterneuburg)
Daniel Loughran (U Bath)
Rachel Newton (KCL, London)