Abelian surfaces with odd bilevel structure

The moduli space of abelian surfaces with polarisation of type (1,t) and a bilevel structure is of general type if t is odd and at least 17.Comment: 21 page

Fundamental groups of toroidal compactifications

We compute the fundamental group of a toroidal compactification of a Hermitian locally symmetric space $D/\Gamma$, without assuming either that $\Gamma$is neat or that it is arithmetic. We also give bounds for the first Betti number.Comment: Final version. Fixes error pointed out by M. Roessler, leading to slightly but significantly changed statements: improved notatio

Abelianisation of orthogonal groups and the fundamental group of modular varieties

We study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms. We show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry, in particular the moduli of K3 surfaces. We give applications to modular forms and to computing the fundamental groups of some moduli spaces

Heisenberg-invariant Kummer surfaces

We study the geometry of Nieto's quintic threefold (Barth & Nieto, J. Alg. Geom. 3, 1994) and the Kummer and abelian surfaces that correspond to special loci.Comment: Plain TeX, 17 pages. Final version, with minor corrections, to appear in Proc. Edinburgh Math. So