23 citations · 56 across the 18 of their papers we have counts for
30 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…
Twisted scalar curvature as a moment map
Ruadhaí Dervan, Thomas Murphy, Julius Ross +2
We develop the moment map theory of the twisted scalar curvature of a Kähler metric. Primarily, we introduce a coupled system of equations on a holomorphic submersion intertwining…
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 universal structure of moment maps in complex geometry
Ruadhaí Dervan, Michael Hallam
We introduce a geometric approach to the construction of moment maps in finite and infinite-dimensional complex geometry. We apply this to two settings: Kähler manifolds and holomo…
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…
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…
Extremal Kähler metrics on blowups
Ruadhaí Dervan, Lars Martin Sektnan
Consider a compact Kähler manifold which either admits an extremal Kähler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point a…
Stability conditions for polarised varieties
Ruadhaí Dervan
We introduce an analogue of Bridgeland's stability conditions for polarised varieties. Much as Bridgeland stability is modelled on slope stability of coherent sheaves, our notion o…
-critical connections and Bridgeland stability conditions
Ruadhaí Dervan, John Benjamin McCarthy, Lars Martin Sektnan
We associate geometric partial differential equations on holomorphic vector bundles to Bridgeland stability conditions. We call solutions to these equations -critical connection…
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…
Uniqueness of optimal symplectic connections
Ruadhaí Dervan, Lars Martin Sektnan
Consider a holomorphic submersion between compact Kähler manifolds, such that each fibre admits a constant scalar curvature Kähler metric. When the fibres admit continuous automorp…
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…
Optimal symplectic connections on holomorphic submersions
Ruadhaí Dervan, Lars Martin Sektnan
The main result of this paper gives a new construction of extremal Kähler metrics on the total space of certain holomorphic submersions, giving a vast generalisation and unificatio…
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.
Extremal metrics on fibrations
Ruadhaí Dervan, Lars Martin Sektnan
Consider a fibred compact Kähler manifold X endowed with a relatively ample line bundle, such that each fibre admits a constant scalar curvature Kähler metric and has discrete auto…
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…
Hermitian Yang-Mills connections on blowups
Ruadhaí Dervan, Lars Martin Sektnan
Consider a vector bundle over a Kähler manifold which admits a Hermitian Yang-Mills connection. We show that the pullback bundle on the blowup of the Kähler manifold at a collectio…
The Kähler-Ricci flow and optimal degenerations
Ruadhaí Dervan, Gábor Székelyhidi
We prove that on Fano manifolds, the Kähler-Ricci flow produces a "most destabilising" degeneration, with respect to a new stability notion related to the H-functional. This answer…
Relative K-stability for Kähler manifolds
Ruadhaí Dervan
We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of relative K-stability for Kähler manifolds, we prove that Kähler manifolds admit…
K-stability for Kähler Manifolds
Ruadhaí Dervan, Julius Ross
We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi f…