| Abstract |
We deal with compact complex manifolds X. Already in the early days of complex
geometry it was realized that it is of fundamental interest to view these as moving
in families, i.e., a fibration π : X → S where π
−1
(s) =: Xs are the manifolds of
interest as s moves in the parameter space S. A first important example, which will
be discussed in the talk, is where Xs is defined as the 0-set of a polynomial whose
coefficients depend on s, e.g., cubics varying in the (projective) plane. Another
important classical example arises when one defines a family X of 1-dimensional
tori by Xs being the quotient of the complex plane, Xs := C/Γs, by a lattice which
is presented by generators which depend on s, e.g., Γs = SpanZ(1, s) where s runs
in the upper halfplane.
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