%0 Journal Article
%A López-Gómez, Julián
%A Sampedro Pascual, Juan Carlos
%T New analytical and geometrical aspects of the algebraic multiplicity
%D 2021
%@ 0022-247X
%U https://hdl.handle.net/20.500.14352/7288
%X 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.
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