In deformation theory certain problems can be solved by surprisingly simple and analytical means. Consider the following problem:

Given complex manifolds X and Y with holomorphic map f : Y -> X, does a first order infinitesimal deformation of f, a given section σ : Y -> f*TX, belong to a deformation of f? If so, σ is called effective.

A special class of fibrebundles, so called Jetbundles are a very useful tool in this discussion. They generalise the notion of the tangent bundle of a manifold. Jetbundles can be used to prove a cohomological criterion for the effectiveness of first order infinitesimal deformations.

In this talk the underlying problem will be explained and an analytic definition of Jetbundles will be given and used for a constructive approach to this abstract problem.

The talk is open to the public. Guests are cordially invited!