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arXiv · 2504.06612

A Hilbert--Mumford criterion for generalised Monge--Amp\`ere equations

Rémi Reboulet
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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.

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Rémi Reboulet. 2025-04-09. A Hilbert--Mumford criterion for generalised Monge--Amp\`ere equations. https://arxiv.org/abs/2504.06612

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