  In this survey article we want to discuss a way of constructing
arithmetically Gorenstein varieties of high codimension. Consider kernel
sheaves B_G of general, generically surjective morphisms G between decomposable
bundles on P^n. The top-dimensional part of the zero-locus of a regular section
of B_G is Gorenstein if B_G has odd rank.
  We show how to implement the construction method in the computer algebra
system Singular and produce some examples of Gorenstein curves and threefolds
in P^6. Finally, we investigate a class of sheaves B_G, where the degeneracy
locus of G does not have the expected codimension.
