Speaker: Alexander Bednarek博士，悉尼大学

Inviter: 简旺键副研究员

Title: Fano Fibrations and Twisted Kahler-Einstein Metrics

Language: English

Time & Venue: 2025.05.26 09:30-10:30 腾讯会议：464-6610-0075

Abstract: The Kahler-Ricci flow on a compact manifold with semi-ample K_X induces a Calabi-Yau fibration over an analytic, projective variety. Due to the work of Tosatti, Weinkove and Yang, it is known that the flow converges in the C^0_loc topology away from the singular fibres of the fibration to a singular twisted Kahler-Einstein metric constructed on the base space. On the other hand, both the Kahler-Ricci flow and continuity method with finite time singularities beginning from a rational initial metric induce a Fano fibration. It has been shown by Yashan Zhang and Zhenlei Zhang that one can again construct a singular Kahler metric on the base space which the continuity method converges to in the C^0_loc topology away from the singular fibres of the fibration. I discuss some upcoming work in which an explicit differential-geometric construction of the Weil-Petersson metric for the Fano fibration is given and show that the base space metric also satisfies a type of twisted Kahler-Einstein equation.