Speaker: 张润泽(法国Nice大学)

Time: 15:00-16:00, Apr.24

Venue: 数学中心研讨室（至善楼602）

Online: Zoom: 811 5638 1768（Password: msrc）

Title: Logarithmic ddbar-lemmata and several geometric applications（线上）

Abstract:

In this talk, we will prove two ddbar-type lemmata on compact Kähler manifolds for logarithmic differential forms with values in the dual of a pseudo-effective line bundle, which partially confirm a conjecture proposed by Xueyuan Wan. The main ingredients in the proofs are the Hodge decomposition for forms that are smooth in conic sense and the de Rham--Kodaira decomposition for conic currents, established by Junyan Cao--Mihai Păun, along with the utilization of two acyclic resolutions of sheaves of logarithmic forms with values in the dual bundle. We then obtain several applications, among which are strengthened results of H. Esnault--E. Viehweg on the degeneracy of the spectral sequence at E_1-stage for projective manifolds associated with the logarithmic de Rham complex, and of L. Katzarkov--M. Kontsevich--T. Pantev on the unobstructed deformations of a very general log projective Calabi--Yau pair, both extended to the broader context of compact Kähler manifolds.