New Analytical and Geometrical Aspects of the Algebraic Multiplicity

2020/12/10 by López-Gómez, Julián, Sampedro, Juan Carlos · 1 citation
#14C17 #47J10 #47J15 #58C40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2012.05671

Abstract

This paper reveals some new analytical and geometrical properties of the generalized algebraic multiplicity, χ, introduced in [7, 5] and further developed in [20, 23, 24]. 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, \mathfrakL(λ).

Cited by

• Spectral Theory and Bezout Theorem

Related

• Spectral Theory and Bezout Theorem
• A bridge between Vector Bundle Theory and Nonlinear Spectral Theory
• Algebraic spectral theory and Serre multiplicity formula
• Serre Intersection Multiplicity Conjecture and Hodge theory
• The Complete Intersection Discrepancy of a Curve II: Families of Curves