This is a sequel to the previous paper [6], which studied connections between the differential geometry of complex projective varieties and certain specific “balanced” embeddings in projective space.… (More)

These are the notes of the course given in Autumn 2007. Two good books (among many): Adams: Lectures on Lie groups (U. Chicago Press) Fulton and Harris: Representation Theory (Springer) Also various… (More)

We consider structures analogous to symplectic Lefschetz pencils in the context of a closed 4–manifold equipped with a “near-symplectic” structure (ie, a closed 2–form which is symplectic outside a… (More)

Since 1982 the use of gauge theory, in the shape of the Yang-Mills instanton equations, has permeated research in 4-manifold topology. At first this use of differential geometry and differential… (More)

Let V be a four-dimensional real vector space with a fixed orientation. Then the wedge product can be viewed, up to a positive factor, as a canonical quadratic form of signature (3, 3) on the… (More)

One of the cornerstones of complex geometry is the link between positivity of curvature and ampleness. Let X be a compact complex manifold and L ! X be a holomorphic line bundle over X. Suppose that… (More)

theory of Lie groups—but many geometric questions lead to non-standard problems which go beyond, or lie on the frontiers of, standard theory. Such questions arise both in reassuringly down-to-earth… (More)

We present a new proof of a result due to Taubes: if (X,ω) is a closed symplectic four-manifold with b+(X) > 1 + b1(X) and λ[ω] ∈ H (X;Q) for some λ ∈ R, then the Poincaré dual of KX may be… (More)