7 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…
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…