  Duality groups of Abelian gauge theories on four manifolds and their
reduction to two dimensions are considered. The duality groups include elements
that relate different space-times in addition to relating different
gauge-coupling matrices. We interpret (some of) such dualities as the
geometrical symmetries of compactified theories in higher dimensions. In
particular, we consider compactifications of a (self-dual) 2-form in 6-D, and
compactifications of a self-dual 4-form in 10-D. Relations with a self-dual
superstring in 6-D and with the type IIB superstring are discussed.
