Abstrakt: Given a complex vector space V of dimension n,
one can look at d-dimensional linear subspaces A in
Alt^2(V), whose elements have constant rank r. The
natural interpretation of A as a vector bundle map
yields some restrictions on the values that r, n and d
can attain. After a brief overview of the subject and
of the main techniques used, I will concentrate on the
case r=n-2 and d=4. I will introduce what used to be the
only known example, by Westwick, and give an explanation
of this example in terms of instanton bundles and the
derived category of P^3. I will then present a new
method that allows one to prove the existence of new
examples of such spaces, and show how this method
applies to instanton bundles of charge 2 and 4.

These results are in collaboration with D.Faenzi and