1,029 research outputs found
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
The moduli space of bilevel-6 abelian surfaces
The moduli space of abelian surfaces with polarisation of type (1,6) and a
bilevel structure has positive Kodaira dimension. By contrast, Mukai has shown
that the moduli space of bilevel-t abelian sufaces is rational for t=2,3,4,5.Comment: 9 pages, plain TeX. Results improved and extended: an error correcte
Fundamental groups of toroidal compactifications
We compute the fundamental group of a toroidal compactification of a
Hermitian locally symmetric space , without assuming either that
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
On some lattice computations related to moduli problems
We show how to solve computationally a combinatorial problem about the
possible number of roots orthogonal to a vector of given length in . We
show that the moduli space of K3 surfaces with polarisation of degree 2d is
also of general type for d=52. This case was omitted from the earlier work of
Gritsenko, Hulek and the second author. We also apply this method to some
related problems. In Appendix A, V. Gritsenko shows how to arrive at the case
d=52 and some others directly.Comment: With an appendix by V. Gritsenk
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
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