New analytical and geometrical aspects of the algebraic multiplicity

This paper reveals some new analytical and geometrical properties of the generalized algebraic multiplicity, χ, introduced in [7], [5] further developed [15], [17], [18]. In particular, it establishes a completely connection between χ concept local intersection index varieties, central device Algebraic Geometry. link Nonlinear Spectral Theory Geometry provides to with deep meaning. Moreover, is characterized through notion determinant Schur operator associated linear path, L(λ).