López-Gómez, JuliánSampedro Pascual, Juan Carlos2023-06-172023-06-172021-05-260022-247X10.1016/j.jmaa.2021.125375https://hdl.handle.net/20.500.14352/7288This 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.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttps://doi.org/10.1016/j.jmaa.2021.125375open access512.7Algebraic multiplicityNonlinear Spectral TheorySchur complementLocal determinantBifurcation equationLocal intersection indexAlgebraic Geometry.Geometria algebraica1201.01 Geometría Algebraica