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19 April 2024
 
  » arxiv » 2006.1530

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A numerical criterion for generalised Monge-Ampere equations on projective manifolds
Ved V. Datar ; Vamsi Pritham Pingali ;
Date 2 Jun 2020
AbstractWe prove that generalised Monge-Ampere equations (a family of PDE which includes the inverse Hessian equations like the J-equation, as well as the Monge-Ampere equation) on projective manifolds have smooth solutions if and only if a numerical criterion is satisfied. As a corollary, we prove a uniform version of a conjecture of Szekelyhidi in the projective case. Our result also includes an equivariant version which can be used to recover existing results on manifolds with large symmetry such as projective toric manifolds.
Source arXiv, 2006.1530
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