9 papers
A birational version of K-stability for big classes
Ruadhaà Dervan, Rémi Reboulet
We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and f…
Filtrations and asymptotic geometry of non-Archimedean norms on section rings
Rémi Reboulet
This article is concerned with the metric study of a construction of Gérardin of the action of the boundary at infinity of the space of norms on a non-Archimedean vector space, an…
Transcendental Okounkov bodies
Tamás Darvas, Rémi Reboulet, David Witt Nyström +2
We show that the volume of transcendental big -classes on compact Kähler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-MustaÅ£Ä and De…
Infinite-dimensional flats in the space of positive metrics on an ample line bundle
Rémi Reboulet, David Witt Nyström
We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded fil…
Flats in the space of Kähler metrics and Okounkov bodies
Rémi Reboulet
We study sufficient conditions for the existence of flat subspaces in the space of continuous plurisubharmonic metrics on a polarised complex projective manifold, relying on the ge…
A Hilbert--Mumford criterion for generalised Monge--Ampère equations
Rémi Reboulet
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…