The International Center for Mathematical Sciences – Sofia (ICMS-Sofia)

presents

ICMS Seminar

30.07.2024, 14:00 Sofia time,

ICMS-Sofia, Room 403

Rational points and Campana points on toric varieties and their subvarieties

Marta Pieropan
Utrecht University

Abstract:
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 transforms a counting problem into an optimization problem on certain polytopes. For rational points on subvarieties of 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.