A Hilbert--Mumford criterion for generalised Monge--Amp\`ere equations
Differential Geometry
2025-04-10 v1 Algebraic Geometry
Abstract
We give a new numerical criterion in the spirit of GIT for existence of solutions to inverse Hessian equations, including in particular the J-equation. Our criterion is formulated in terms of stability of pairs in the sense of Paul. To that end, we build on previous work of the author with Dervan, and generalise a result of Zhang, proving isometry between generalised Chow line bundles and mixed Deligne pairings.
Cite
@article{arxiv.2504.06612,
title = {A Hilbert--Mumford criterion for generalised Monge--Amp\`ere equations},
author = {Rémi Reboulet},
journal= {arXiv preprint arXiv:2504.06612},
year = {2025}
}