On the modified $J$-equation
Time: 2022-09-13
Published By: Wenqiong Li
Speaker(s): Ryosuke Takahashi (Kyushu University)
Time: 09:00-10:00 September 21, 2022
Venue: Online
Abstract:
Speaker:
Zoom:
https://us06web.zoom.us/j/84270050537?pwd=YXNnaTBrLzRBOWhXU25GUjkzNTlyUT09
ID: 842 7005 0537
Passcode: 851096
In this talk, we consider the modified $J$-equation introduced by Li-Shi. This is a complex Hessian equation including Hamiltonians of holomorphic vector fields, and coincides with the usual $J$-equation introduced by Donaldson and X. Chen when the vector field vanishes. We show that the solvability of the modified $J$-equation is equivalent to the coercivity of the modified $J$-functional on general compact K\"ahler manifolds. On toric manifolds, we give a numerical necessary and sufficient condition for the existence of solutions, which extends the results of Collins-Sz\'ekelyhidi.
Speaker:
Ryosuke Takahashi is currently an assistant professor at Kyushu University. He got his Ph.D. at Nagoya University in 2015 under the supervision of Prof. Ryoichi Kobayashi. His research interests are differential geometry and geometric analysis.
Zoom:
https://us06web.zoom.us/j/84270050537?pwd=YXNnaTBrLzRBOWhXU25GUjkzNTlyUT09
ID: 842 7005 0537
Passcode: 851096
