报告人： 刘海东 博士后 (北京大学)
时间：2021年6月23日 15:30-16:30
地点： 精正楼307室


摘要：On K-trivial varieties (e.g. Calabi-Yau manifolds, hyperkalher manifolds), the well-known abundance 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 variety 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. 
For strictly nef divisors, the generalized abundance conjecture is also known as ampleness conjecture, that is, any strictly nef divisor on a K-trivial manifold is ample. I will answer partially the ampleness conjecture in dimension 3; I will also show the ampleness conjecture holds true surprisingly in dimension 4 (in the strict sense).
The 3-dimensional case is a joint work with Roberto Svaldi; the 4-dimensional case is a joint work with Shin-ichi Matsumura.



邀请人：顾怡