  We introduce the strength for sections of a line bundle on an algebraic
variety. This generalizes the strength of homogeneous polynomials that has been
recently introduced to resolve Stillman's conjecture, an important problem in
commutative algebra. We establish the first properties of this notion and give
some tool to obtain upper bounds on the strength in this framework. Moreover,
we show some results on the usual strength such as the reducibility of the set
of strength two homogeneous polynomials.
