On the solvability of general inverse $\sigma_k$ equations

BIMSA-YMSC Geometry and Dynamics Seminar

Organizer：

Yu-Wei Fan (YMSC)

Speaker：

Chao-Ming Lin (Ohio State University)

Time：

Wed., 9:00-10:00 am, May 28, 2025

Online：

Zoom Meeting ID: 815 762 8413Passcode: BIMSA

Title：

On the solvability of general inverse $\sigma_k$ equations

Abstract：

In this talk, first, I will introduce general inverse $\sigma_k$ equations in Kähler geometry. Some classical examples are the complex Monge–Ampère equation, the J-equation, the complex Hessian equation, and the Leung—Yau—Zaslow (dHYM) equation. Second, by introducing some new real algebraic geometry techniques, we can consider more complicated general inverse $\sigma_k$ equations. Last, analytically, we study the solvability of these complicated general inverse $\sigma_k$ equations.