3 citations · 5 across the 11 of their papers we have counts for
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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…
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…
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…
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…