Weighted K-stability and special metrics in Kahler and Sasaki geometry
发布时间：2021年09月06日
浏览次数：5153
发布者: Wenqiong Li
主讲人： Abdellah Lahdili (BICMR)
活动时间： 从 2021-09-08 15:00 到 16:00
场地： Online
Date: Wednesday, September 8, 2021
Time: 3:00 pm to 4:00 pm
Venue: Online
Description:
For a compact weighted extremal Kahler manifold we show the strict positivity of the weighted Donaldson-Futaki invariant of any non-product equivariant smooth Kähler test configuration with reduced central fibre, a property also known as weighted K-stability on such test configurations. This provides a vast extension and a unification of a number of results concerning Kahler metrics satisfying special curvature conditions, including constant scalar curvature Kahler metrics, extremal Kahler metrics, Kahler-Ricci solitons and their weighted extensions. For a class of fibre-bundles, we use the recent results of Chen-Cheng, He in order to characterize the existence of extremal Kahler metrics, in terms of the coercivity of the weighted Mabuchi energy of the fibre. As an application, we establish a Yau-Tian-Donaldson correspondence for weighted extremal Kahler metrics on sphere bundles over the product of cscK Hodge manifolds. This talk is based on joint work with Vestislav Apostolov and Simon Jubert.
Time: 3:00 pm to 4:00 pm
Venue: Online
Description:
For a compact weighted extremal Kahler manifold we show the strict positivity of the weighted Donaldson-Futaki invariant of any non-product equivariant smooth Kähler test configuration with reduced central fibre, a property also known as weighted K-stability on such test configurations. This provides a vast extension and a unification of a number of results concerning Kahler metrics satisfying special curvature conditions, including constant scalar curvature Kahler metrics, extremal Kahler metrics, Kahler-Ricci solitons and their weighted extensions. For a class of fibre-bundles, we use the recent results of Chen-Cheng, He in order to characterize the existence of extremal Kahler metrics, in terms of the coercivity of the weighted Mabuchi energy of the fibre. As an application, we establish a Yau-Tian-Donaldson correspondence for weighted extremal Kahler metrics on sphere bundles over the product of cscK Hodge manifolds. This talk is based on joint work with Vestislav Apostolov and Simon Jubert.
Speaker：
Abdellah Lahdili
北京国际数学研究中心博士后，师从田刚教授。2019年博士毕业于魁北克大学蒙特利尔分校(UQAM)，师从Vestislav Apostolov教授。
Research: Kahler Geometry
Research: Kahler Geometry
Zoom:
https://us02web.zoom.us/j/87227618837?pwd=bEVjTU0vUkMvdHA1UUVOaElGVTI2Zz09
ID: 872 2761 8837
Code: 157742
