23 citations · 56 across the 18 of their papers we have counts for
16 papers · 1 filter
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 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…
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…
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…
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…
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…
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…
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…
A finite dimensional approach to Donaldson's J-flow
Ruadhaí Dervan, Julien Keller
We define a quantisation of the J-flow over a projective complex manifold. As corollaries, we obtain new proofs of uniqueness of critical points of the J-flow and that these critic…
Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
Ruadhaí Dervan
We give a criterion for the coercivity of the Mabuchi functional for general Kähler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian…
Uniform stability of twisted constant scalar curvature Kähler metrics
Ruadhaí Dervan
We introduce a norm on the space of test configurations, which we call the minimum norm. We conjecture that uniform K-stability with respect to this norm is equivalent to the exist…