Time: 15:30-18:00, December 30/31 2024, January 2 2025
ZOOM ID: 962 3094 8410
PASSCODE: 846653
Host: Xin Fu, ITS
Speaker: Runze Zhang, Université Côte d'Azur & Wuhan University
Title: Logarithmic ddbar-lemma and several geometric applications
Abstract: In this series of three talks, I will present our recent results on a ddbar lemma on compact Kähler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line bundle, which confirms a conjecture proposed by X. Wan.
I will also discuss several applications, including strengthened results by H. Esnault and E. Viehweg on the degeneracy of the spectral sequence at the $E_1$-stage for projective manifolds associated with the logarithmic de Rham complex, and by L. Katzarkov, M. Kontsevich, and T. Pantev on the unobstructed locally trivial deformations of a projective generalized log Calabi–Yau pair with some weights. Both results are extended to the broader context of compact Kähler manifolds.
Furthermore, I will outline the Kähler version of an injectivity theorem originally formulated by F. Ambro in the algebraic setting. Notably, while O. Fujino also addressed the Kähler case, our proof takes a different approach, avoiding relia\nce on the theory of mixed Hodge structures for cohomology with compact support.
