Cohomology of Complex Torus Bundles Associated to Cocycles
Printed: Aug 2003
Equivariant holomorphic maps of Hermitian symmetric domains into
Siegel upper half spaces can be used to construct families of
abelian varieties parametrized by locally symmetric spaces, which
can be regarded as complex torus bundles over the parameter spaces.
We extend the construction of such torus bundles using 2-cocycles of
discrete subgroups of the semisimple Lie groups associated to the
given symmetric domains and investigate some of their properties.
In particular, we determine their cohomology along the fibers.
14K10 - Algebraic moduli, classification [See also 11G15]
14D06 - Fibrations, degenerations
14F99 - None of the above, but in this section