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Geometry of four-manifolds
1. Four-manifolds 2. Connections 3. The Fourier transform and ADHM construction 4. Yang-Mills moduli spaces 5. Topology and connections 6. Stable holomorphic bundles over Kahler surfaces 7. ExcisionExpand
Scalar Curvature and Stability of Toric Varieties
We define a stability condition for a polarised algebraic variety and state a conjecture relating this to the existence of a Kahler metric of constant scalar curvature. The main result of the paperExpand
Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
On presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels. Soit une surface algebrique projective X qui a un plongement donne X≤CP N et soit ωExpand
Scalar Curvature and Projective Embeddings, I
We prove that a metric of constant scalar curvature on a polarised Kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings; satisfying a condition introducedExpand
An application of gauge theory to four-dimensional topology
Soit X une u-variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee Q est definie positive. Alors cette forme est equivalente, sur les entiers, a la formeExpand
Polynomial invariants for smooth four-manifolds
THE TRADITIONAL methods of geometric topology have not given a clear picture of the classification of smooth 4-manifolds. This gap has been partially bridged by the introduction into 4-manifoldExpand
Kähler Metrics with Cone Singularities Along a Divisor
We develop some analytical foundations for the study of Kahler metrics with cone singularities in codimension one. The main result is an analogue of the Schauder theory in this setting. In the laterExpand
Twisted harmonic maps and the self-duality equations
Si M est une surface de Riemann compacte, on utilise des resultats de la theorie des applications harmoniques pour trouver une solution aux equations d'auto-dualite associees a une representationExpand