Explicit bounds on foliated surfaces and the Poincaré problem

par Stefania Vassiliadis (Kings College London)

jeudi 22 oct. 2026, 10:15 → 11:30 Europe/Paris

Extending the approaches of Spicer-Svaldi and Pereira-Svaldi, we study

the set of pseudo-effective thresholds of adjoint foliated structures on surfaces. We establish an explicit positive lower bound for the pseudo-effective threshold, which in turn yields effective birationality results for adjoint divisors of the form KF + tKX . As an application, we refine a bound on the degree of general leaves of foliations of general type, obtaining a bound that is linear in the genus of the general leaf.