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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 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.
Stability conditions in geometric invariant theory
Ruadhaà 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…
Arcs, stability of pairs and the Mabuchi functional
Ruadhaà 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…