131 citations · 140 across the 4 of their papers we have counts for
5 papers
Lower bounds on the Calabi functional
S. K. Donaldson
The main result of this paper shows that "test configurations" give new lower bounds on the norm of the scalar curvature on a Kahler manifold. This is closely analogous to…
Scalar curvature and projective embeddings, II
S. Donaldson
The paper uses the technique of finite-dimensional approximation to show that a constant scalr curvature Kahler metric (on a polarised algebraic variety without holomorphic vector…
Interior estimates for solutions of Abreu's equation
S. K. Donaldson
The paper develops various estimates for solutions of a fourth order nonlinear PDE, which corresponds to prescribing the scalar curvature of a toric Kahler metric.
Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves
D. Auroux, S. K. Donaldson, L. Katzarkov
We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide…
Lefschetz pencils and the canonical class for symplectic 4-manifolds
Simon Donaldson, Ivan Smith
We present a new proof of a result due to Taubes: if X is a closed symplectic four-manifold with b_+(X) > 1+b_1(X) and with some positive multiple of the symplectic form a rational…