Complexity of the computation of linear projections

Our main result is that the complexity of computing linear projections of a n equidimensional, but lion necessarily reduced, curve C in P-K(n), (or equ ivalently the degree-complexity of the Grobner basis computation for elimin ation orders) Bus its maximal value, namely Bayer's bound m(o), if and only if the smallest linear subspace containing C is a plane. If this is so, m( o) coincides with the degree of C and with the degree-complexity of the rev erse lexicographic ordering.