Deformation limit and invariance of plurigenera of Moishezon varieties

时间：2022年9月21日9:00-10：00

地点：六号楼2楼报告厅

摘要: This talk mainly concerns two topics on the deformations of Moishezon varieties. The first one is a long-standing conjecture that the smooth deformation limit of projective or Moishezon manifolds is Moishezon. We will prove this conjecture under some mild condition on the limit fiber. The second one is deformation invariance of plurigenera, particularly on a question of Demailly whether a smooth family of nonsingular projective varieties admits the deformation invariance of plurigenera. We confirm this more generally for a smooth fiberwise Moishezon family, and also prove a flat family case. And several more recent progresses and applications are also discussed. This talk is mainly based on several joint works with I-Hsun Tsai, Yi Li and Runze Zhang.