中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人：刘海东（北京大学）
题 目：On Generalised Abundance
时 间：2021.05.18（星期二），13:30-14:30
地 点：晨兴 410
摘 要：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.
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