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Learning Seminar on PDE and Applications

Complex hessian quotient equations

Jian Song, Rutgers University

Date & time: Tuesday, 11 August 2020 at 1:40PM - 3:40PM

Abstract: The J-flow is proposed by Donaldson to study symplectomorphisms of a Kaher manifold. The J-equation, critical equation of the J-flow, corresponds to a standard complex hessian quotient equation. The global J-equation does not always admit a smooth solution due to topological obstructions. We review both the analytic and topological conditions for solving the J-equation. These equivalent conditions are natural analogues of the Nakai criterion in algebraic geometry.

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