4 papers
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…
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 polaris…
Extremal Kähler metrics on blowups
Ruadhaà 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…
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 cla…