There are embeddings of complex abelian surfaces in P but it was shown by Van de Ven in [17] that no abelian d-fold can be embedded in P if d ≥ 3. Hulek [9], Lange [13], Birkenhake [4] and Bauer and… (More)

We show that the coarse moduli space R5 of étale double covers of curves of genus 5 over the complex numbers is unirational. We give two slightly different arguments, one purely geometric and the… (More)

The moduli space A g of principally polarised abelian g-folds is a quasi-projective variety. It has a natural projective compactification, the Satake compactification, which has bad singularities at… (More)

The geometry of moduli spaces of complex abelian varieties and of compactifications of those moduli spaces has been the object of much study in the last few years. Given such a compactified moduli… (More)

Abelian surfaces over C with a polarisation of type (1, t), t a positive integer, are parametrised by a coarse moduli space At which is a quasiprojective variety. In this paper we shall concentrate… (More)

For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than 19. In this paper we obtain the first… (More)

In fact it is enough to prove this for one such X, since any two X have the same fundamental group. If p = 5 or 7 then X is known to be rational and therefore simply connected. For p = 5 this goes… (More)

We study degenerations of Kummer surfaces associated to certain divisors in Nieto’s quintic threefold and show how they arise from boundary components of a suitable toroidal compactification of the… (More)

The moduli space of abelian surfaces with a polarisation of type (1, p 2) for p a prime was studied by O'Grady in [O'G], where it is shown that a compactification of this moduli space is of general… (More)