3 citations · 5 across the 11 of their papers we have counts for
12 papers
A birational version of K-stability for big classes
Ruadhaí 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, and…
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…
Arcs, stability of pairs and the Mabuchi functional
Ruadhaí Dervan, Rémi Reboulet
We prove various results involving arcs - which generalise test configurations - within the theory of K-stability. Our main result characterises coercivity of the Mabuchi functiona…
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…
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-Mustaţă and Deng.…
The birational geometry of GIT quotients
Ruadhaí Dervan, Rémi Reboulet
Geometric Invariant Theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by…
Ding stability and Kähler-Einstein metrics on manifolds with big anticanonical class
Ruadhaí Dervan, Rémi Reboulet
We introduce a notion of uniform Ding stability for a projective manifold with big anticanonical class, and prove that the existence of a unique Kähler-Einstein metric on such a ma…
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…
The space of finite-energy metrics over a degeneration of complex manifolds
Rémi Reboulet
Given a degeneration of compact projective complex manifolds over the punctured disc, with meromorphic singularities, and a relatively ample line bundle on , we study sp…
Plurisubharmonic geodesics in spaces of non-Archimedean metrics of finite energy
Rémi Reboulet
Given a polarized projective variety (X,L) over any non-Archimedean field, assuming continuity of envelopes, we show that the space of finite-energy metrics on L is a geodesic metr…
The asymptotic Fubini-Study operator over general non-Archimedean fields
Rémi Reboulet
Given an ample line bundle over a projective -variety , with a non-Archimedean field, we study limits of non-Archimedean metrics on associated t…