# A numerical criterion for generalised Monge-Ampère equations on projective manifolds

@article{Datar2021ANC,
title={A numerical criterion for generalised Monge-Amp{\e}re equations on projective manifolds},
author={Ved V. Datar and Vamsi Pingali},
journal={Geometric and Functional Analysis},
year={2021}
}
• Published 2 June 2020
• Mathematics
• Geometric and Functional Analysis
We prove that generalised Monge-Ampere equations (a family of equations which includes the inverse Hessian equations like the J-equation, as well as the Monge-Ampere equation) on projective manifolds have smooth solutions if certain intersection numbers are positive. As corollaries of our work, we improve a result of Chen (albeit in the projective case) on the existence of solutions to the J-equation, and prove a conjecture of Szekelyhidi in the projective case on the solvability of inverse…

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