8 papers
The constant scalar curvature Kähler condition is very general
Ruadhaà 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 uni…
A birational version of K-stability for big classes
Ruadhaà 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 universal structure of moment maps in complex geometry
Ruadhaà 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 holom…
Twisted scalar curvature as a moment map
Ruadhaà 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 birational geometry of GIT quotients
Ruadhaà 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…
Moduli of polarised manifolds via canonical Kähler metrics
Ruadhaà 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.