(joint with Giorgio Ottaviani and Chris Peterson)
The main goal of this talk is to present an inductive procedure to check
whether the secant variety of a given Segre variety has the expected
dimension. The basic idea behind this procedure is to reduce the computation
of the dimension of the secant variety of the Segre variety to the
computation of the dimension of a collection of partial secant varieties
of lower dimensional Segre varieties. The method is built around a
sequence of specializations and in the process, a high dimensional problem
is reduced, to a collection of lower dimensional problems. In this talk,
we will discuss examples to illustrate how to use this technique.