32 citations · 61 across the 9 of their papers we have counts for
10 papers
Finiteness and rigidity of optimal destabilizing subvarieties for the J-equation
P. Sivaram, Zakarias Sjöström Dyrefelt
We prove that when the J-equation does not admit a smooth solution, there is always only a finite number of obstructing optimally destabilizing curves and divisors on compact Kähle…
CscK metrics on birational models of projective varieties
Zakarias Sjöström Dyrefelt
We prove that every complex projective variety is birational to a smooth projective manifold admitting a constant scalar curvature Kähler (cscK) metric. For any smooth projective v…
Wall-chamber decompositions for generalised Monge-Ampère equations
Sohaib Khalid, Zakarias Sjöström Dyrefelt
Generalised Monge-Ampère equations form a large class of PDE including Donaldson's J-equation, inverse Hessian equations, some supercritical deformed Hermitian-Yang Mills equations…
The set of destabilizing curves for deformed Hermitian Yang-Mills and Z-critical equations on surfaces
Sohaib Khalid, Zakarias Sjöström Dyrefelt
We show that on any compact Kähler surface existence of solutions to the Z-critical equation can be characterized using a finite number of effective conditions, where the number of…
Openness of uniform K-stability in the Kähler cone
Zakarias Sjöström Dyrefelt
We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the Kähler cone of any compact K…
Existence of cscK metrics on smooth minimal models
Zakarias Sjöström Dyrefelt
Given a compact Kähler manifold it is interesting to ask whether it admits a constant scalar curvature Kähler (cscK) metric. In this short note we show that there always exist…
Optimal lower bounds for Donaldson's J-functional
Zakarias Sjöström Dyrefelt
In this paper we provide an explicit formula for the optimal lower bound of Donaldson's J-functional, in the sense of finding explicitly the optimal constant in the definition of c…
A Partial Comparison of Stability Notions in Kähler Geometry
Zakarias Sjöström Dyrefelt
In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of intere…
On K-polystability of cscK manifolds with transcendental cohomology class
Zakarias Sjöström Dyrefelt
In this paper we study K-polystability of arbitrary (possibly non-projective) compact Kähler manifolds admitting holomorphic vector fields. As a main result, we show that existence…
K-semistability of cscK manifolds with transcendental cohomology class
Zakarias Sjöström Dyrefelt
We prove that constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class are K-semistable, naturally generalising the situation for polarised manifolds.…