  We construct explicit examples of elementary extremal contractions, both
birational and of fiber type, from smooth projective n-dimensional varieties,
n\geq 4, onto smooth projective varieties, arising from classical projective
geometry and defined over sufficiently small fields, not necessarily
algebraically closed.
  The examples considered come from particular special homaloidal and
subhomaloidal linear systems, which usually are degenerations of general
phenomena classically investigated by Bordiga, Severi, Todd, Room, Fano, Semple
and Tyrrell and more recently by Ein and Shepherd-Barron.
  The first series of examples is associated to particular codimension 2
determinantal smooth subvarieties of P^m, 3\leq m\leq 5. We get another series
of examples by considering special cubic hypersurfaces through some surfaces in
P^5, or some 3-folds in P^7 having one apparent double point. The last examples
come from an intriguing birational elementary extremal contraction in dimension
6, studied by Semple and Tyrrell and fully described in the last section.
