多复变与复几何学术活动

中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

多复变与复几何学术活动

Some Topics in Several Complex Variables

报告人：饶胜 (武汉大学)
题  目：Projective, Moishezon, and Kähler Loci of Family I
时  间：7月10日15:00-17:00
地  点：N913
摘 要： This presentation focuses on the projective, Moishezon, and Kähler loci of a family. We begin by addressing a long-standing conjecture that states the holomorphic deformation limit of projective or Moishezon manifolds is Moishezon. We present D. Popovici's current theoretical proof in the projective case, and our distinct proof, jointly developed with I-Hsun Tsai, from the perspective of Grauert's direct image theory in the Moishezon case. Both sets of results are subject to additional conditions imposed by the central fiber. If time permits, we will also discuss the closely related deformation invariance of plurigenera, specifically addressing Demailly's question of whether a smooth family of nonsingular projective varieties exhibits the deformation invariance of plurigenera. As a direct application of our work on deformation limits, we provide a more general confirmation for a smooth fiberwise Moishezon family, and also establish a case for flat families. This presentation is primarily based on several collaborative works with I-Hsun Tsai.

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报告人：王谢平 (中国科学技术大学)
题  目：L2 extension theorem and removable singularities of plurisubharmonic functions
时  间：7月10日18:30-20:30
地  点：N913
摘 要： We will talk about a removable singularity theorem for psh functions across a compact complete pluripolar set in Stein manifolds. The proof of the theorem involves a version of the Ohsawa-Takegoshi L2 extension theorem on complete Kähler manifolds and some basic geometric measure theory.