Complex Geometry Talk
Speaker: Dr. Ramesh Mete, IIT Bombay
Host: Saikat Mazumdar
Title: Twisted and coupled cscK metrics on ruled surfaces
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, October 22
Venue: Ramanujan Hall
Abstract: First we recall the standard canonical metrics in K\"{a}hler geometry. A K\"{a}hler metric is called a constant scalar curvature K\"{a}hler (cscK in short) metric if its scalar curvature is constant. The set of all cscK metrics include the set of all K\"{a}hler-Einstein metrics. Stoppa (2009) introduced the twisted cscK equation by twisting the cscK equation with another equation, called the J-equation. Datar and Pingali (2020) introduced coupled cscK metrics generalizing coupled K\"{a}hler-Einstein metrics defined by Hultgren and Witt Nystr\"{o}m (2019). We study the existence problem of twisted (and coupled) cscK metrics on ruled surfaces using Calabi ansatz. As an application, we give a bound for the Chen-Cheng (2021) invariant on ruled surfaces