Abstract: The J-functional is related to the properness of the K-energy, its critical point equation is a type of the complex Hessian quotient equation, called J-equation. Unlike its relatives such as Monge–Ampère equation and complex Hessian equation, there exist some obstructions to resolve it on Kähler manifolds. I will report the very recently work of T. Collins and G. Székelyhidi. They found a sufficient and necessary condition for resolving the J-equation on toric manifolds, by the continuation method and induction for dimension.

Time: 10:10am-12:00pm, Tuesday, Dec. 30

Place: Room 29, Quan Zhai, BICMR

Speaker: YAO Yi, Nanjing University