  By analyzing the local and infinitesimal behavior of degenerating polarized
variations of Hodge structure the notion of infinitesimal variation of Hodge
structure at infinity is introduced. It is shown that all such structures can
be integrated to polarized variations of Hodge structure and that, conversely,
all are limits of infinitesimal variations of Hodge structure (IVHS) at finite
points. As an illustration of the rich information encoded in this new
structure, some instances of the maximal dimension problem for this type of
infinitesimal variation are presented and contrasted with the "classical" case
of IVHS at finite points.
