Volume of varieties, fibrations, and foliations

par Luca Tasin (Università di Milano)

jeudi 28 mai 2026, 10:30 → 11:30 Europe/Paris

The volume is a fundamental birational invariant of a smooth projective variety X. It measures the asymptotic growth of pluricanonical forms and, when X is minimal, it coincides with the top self-intersection number of K_X​.
A striking theorem of Hacon–McKernan–Xu shows that the volume of a log canonical variety of general type is uniformly bounded away from zero in fixed dimension. In this talk I will discuss analogous questions for fibrations and foliations. I will present recent results, examples, and open problems arising from joint works with Codogni–Patakfalvi and Spicer.