Computing the α-Futaki character

Differential Geometry Seminar

Organizers：

Jialong Deng, Akito Futaki

Speaker：

Kartick Ghosh (Tata Institute of Fundamental Research, Mumbai)

Time：

Tues., 21:00-22:00, Mar. 11, 2025

Online：

Zoom Meeting ID: 276 366 7254

Passcode: YMSC

Title:

Computing the α-Futaki character

Abstract：

Alvarez-Consul–Garcia-Fernandez–Garcia-Prada introduced the Kahler-Yang-Mills equations (coupled equations for a Kahler metric and a metric on a holomorphic vector bundle ). They also introduced the α-Futaki character, an analog of the Futaki character, as an obstruction to the existence of solutions of the Kahler-Yang-Mills equations. In this talk, we will prove a formula for the α-Futaki character for certain ample line bundles over toric manifolds. We will then compute the α-Futaki character in some cases and compare it with the known existence result of Keller–Tønnesen-Friedman.