New analytical and geometrical aspects of the algebraic multiplicity

Abstract

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