23 citations · 56 across the 18 of their papers we have counts for
14 papers · 1 filter
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…
The constant scalar curvature Kähler condition is very general
Ruadhaí Dervan
Recent work of Trusiani implies that the existence of a constant scalar curvature Kähler metric on a smooth polarised variety with discrete automorphism group is equivalent to unif…
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…
On divisorial stability of finite covers
Ruadhaí Dervan, Theodoros Stylianos Papazachariou
Divisorial stability of a polarised variety is a stronger - but conjecturally equivalent - variant of uniform K-stability introduced by Boucksom-Jonsson. Whereas uniform K-stabilit…
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…
Stability conditions in geometric invariant theory
Ruadhaí Dervan
We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads…
Valuative stability of polarised varieties
Ruadhaí Dervan, Eveline Legendre
Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of quantities associated to valuations, which has been essential to all recent progress in the…
Moduli theory, stability of fibrations and optimal symplectic connections
Ruadhaí Dervan, Lars Martin Sektnan
K-polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical Kähler metrics on polarised varieties, and, on the other hand, conjecturally giv…
K-semistability of optimal degenerations
Ruadhaí Dervan
K-polystability of a polarised variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature Kähler metric. When a variety is K-un…
Moduli of polarised manifolds via canonical Kähler metrics
Ruadhaí Dervan, Philipp Naumann
We construct a moduli space of polarised manifolds which admit a constant scalar curvature Kähler metric. We show that this space admits a natural Kähler metric.
Stable maps in higher dimensions
Ruadhaí Dervan, Julius Ross
We formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-st…
On K-stability of finite covers
Ruadhaí Dervan
We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting Kähler-Einstein metrics, including…
Non-reductive automorphism groups, the Loewy filtration and K-stability
Giulio Codogni, Ruadhaí Dervan
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, whi…
Alpha invariants and K-stability for general polarisations of Fano varieties
Ruadhaí Dervan
We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian's alpha invariant, which uses the log canonical threshold to measure singulari…