7 citations · 16 across the 12 of their papers we have counts for
15 papers
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…
Constant scalar curvature Kähler metrics and semistable vector bundles
Annamaria Ortu, Lars Martin Sektnan
We give a necessary and sufficient condition for the projectivisation of a slope semistable vector bundle to admit constant scalar curvature Kähler (cscK) metrics in adiabatic clas…
On the Futaki invariant of Fano threefolds
Lars Martin Sektnan, Carl Tipler
We study the zero locus of the Futaki invariant on K-polystable Fano threefolds, seen as a map from the Kähler cone to the dual of the Lie algebra of the reduced automorphism group…
Analytic K-semistability and local wall-crossing
Lars Martin Sektnan, Carl Tipler
For a small polarised deformation of a constant scalar curvature Kähler manifold, under some cohomological vanishing conditions, we prove that K-polystability along nearby polarisa…
Extremal metrics on the total space of destabilising test configurations
Lars Martin Sektnan, Cristiano Spotti
We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable Kähler manifolds. This produces infinitely many new examples o…
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…
-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…
Hermitian Yang-Mills connections on pullback bundles
Lars Martin Sektnan, Carl Tipler
We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under som…
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…
Blowing up extremal Poincaré type manifolds
Lars Martin Sektnan
We prove a version of the Arezzo-Pacard-Singer blow-up theorem in the setting of Poincaré type metrics. We apply this to give new examples of extremal Poincaré type metrics. A key…
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…
Extremal Kähler Poincaré type metrics on toric varieties
Vestislav Apostolov, Hugues Auvray, Lars Martin Sektnan
We develop a general theory for the existence of extremal Kähler metrics of Poincaré type in the sense of Auvray, defined on the complement of a toric divisor of a polarized toric…
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…
An investigation of stability on certain toric surfaces
Lars Martin Sektnan
We investigate the relationship between stability and the existence of extremal Kähler metrics on certain toric surfaces. In particular, we consider how log stability depends on we…