Given a square implicit DAE system, we construct
by means an algorithm of controlled complexity an equivalent system
which consists simply in a vector field over an algebraic hypersurface
(a so-called, semi-explicit DAE system).
The procedure is based on the computation of a geometric resolution "a
la Kronecker" of a suitable algebraic variety in a jet space associated
to the input DAE system.
(A joint work with L. D'Alfonso, G. Jeronimo, F. Ollivier et A. Sedoglavic)