Peak sections and Bergman kernels on complex hyperbolic cusps

par Shengxuan Zhou (IMT)

jeudi 9 janv. 2025, 10:30 → 11:30 Europe/Paris

The asymptotic behavior of Bergman kernel on Kahler manifold has been studied by Tian, Ruan, Zelditch, Catlin, Ma, Marinescu and many others since 1990. The works related to Bergman kernel plays an important role in complex geometry. In this talk, we will introduce a way to localize the Bergman kernel by using peak sections. As an application, we consider the asymptotic behavior of Bergman kernels on complex hyperbolic cusps. This generalizes a result of Auvray-Ma-Marinescu.

 

References:

[1] Auvray, H., Ma, X. & Marinescu, G. Bergman kernels on punctured Riemann surfaces. Math. Ann. 379, 951–1002 (2021).

[2] Auvray, H., Ma, X. & Marinescu, G. Quotient of Bergman kernels on punctured Riemann surfaces. Math. Z. 301, 2339–2367 (2022).

[3] Zhou, S. Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps. Math. Ann. 390, 1973–2041 (2024).