Injectivity theorem for generalised pairs on surfaces

报告人：Qu Santai(曲三太), Institute of Geometry and Physics, University of Science and Technology of China

摘要：In this talk, I will survey some recent progress about Kollar’s injectivity theorem on cohomologies. In the category of generalised pairs, we show that the injectivity theorem holds for projective generalised pairs with mild singularities when the nef part of the generalised pair is b-abundant. Moreover, by applying the methods from complex analytic geometry, we show that the injectivity theorem holds for generalised Kawamata log terminal generalised pairs on projective surfaces without any extra conditions on the nef parts of the generalised pairs.

时间：2023-12-26 09:00-10:00

地点：Room A-103, TSIMF

degenerations of polarized log Calabi--Yau pairs

报告人：Jiao Junpeng(焦骏鹏), Tsinghua University

摘要：Given a family of log pairs over a smooth curve whose general fiber is a log Calabi--Yau pair in a fixed bounded family, suppose there exists a divisor on the family whose restriction on a general fiber is ample with bounded volume, we show that, if the total space of the family has relatively trivial log canonical divisor and the special fiber has slc singularities, then every irreducible component of the special fiber is birationally bounded.

时间：2023-12-26 10:30-11:30

地点：Room A-103, TSIMF