Singular del Pezzo surfaces that are equivariant compactifications

We determine which singular del Pezzo surfaces are equivariant compactifications of G_a^2, to assist with proofs of Manin's conjecture for such surfaces. Additionally, we give an example of a singular quartic del Pezzo surface that is an equivariant compactification of a semidirect product of G_a and G_m.Comment: 14 pages, main result extended to non-closed ground field

Complement in the pathogenesis of Alzheimer's disease

The emergence of complement as an important player in normal brain development and pathological remodelling has come as a major surprise to most scientists working in neuroscience and almost all those working in complement. That a system, evolved to protect the host against infection, should have these unanticipated roles has forced a rethink about what complement might be doing in the brain in health and disease, where it is coming from, and whether we can, or indeed should, manipulate complement in the brain to improve function or restore homeostasis. Complement has been implicated in diverse neurological and neuropsychiatric diseases well reviewed elsewhere, from depression through epilepsy to demyelination and dementia, in most complement drives inflammation to exacerbate the disease. Here, I will focus on just one disease, the most common cause of dementia, Alzheimer’s disease. I will briefly review the current understanding of what complement does in the normal brain, noting, in particular, the many gaps in understanding, then describe how complement may influence the genesis and progression of pathology in Alzheimer’s disease. Finally, I will discuss the problems and pitfalls of therapeutic inhibition of complement in the Alzheimer brain