Academy of Mathematics and Systems Science, CAS Colloquia & Seminars | Speaker: | 刘海东,北京大学 | Inviter: | | Title: | On Generalised Abundance | Time & Venue: | 2021.05.18 13:30-14:30 晨兴 410 | Abstract: | One of the central problems in modern birational geometry is the so-called abundance conjecture. For K-trivial varieties (e.g. Calabi-Yau manifolds, hyperkalher manifolds), this conjecture is expected to hold in even greater generality, which is the so-called generalised abundance conjecture. It predicts that a nef divisor on a K-trivial varieties is semiample. Generalised abundance conjecture is only known to hold in dimension at most 2. In dimension 3 or higher, only very few cases of the conjecture have been verified. In this talk, I will show some progress on generalised abundance conjecture in dimension 3. As applications, I will explain how to use these results to study the ampleness of strictly nef divisors, which answers partially a conjecture of Serrano in dimension 3; I will also show how the existence of rational curves relates to the generalise abundance, which proves Oguiso’s conjecture in dimension 3 except very few cases. Part of this is a joint work with Roberto Svaldi. | | | |