Spectral Theory and Bezout Theorem

TL;DR

This paper explores the deep connection between eigenvalue multiplicity in spectral theory and the local intersection index in algebraic geometry, revealing a novel relationship between these mathematical concepts.

Contribution

It uncovers a previously unnoticed link between spectral multiplicity and intersection theory, enriching the understanding of both areas.

Findings

Established a formal relationship between algebraic multiplicity and intersection index.

Provided new insights into the geometric interpretation of eigenvalue multiplicity.

Bridged concepts from spectral theory and algebraic geometry.

Abstract

This note investigates the hidden relationship between the concept of algebraic multiplicity of an eigenvalue and the local intersection index of algebraic varieties.