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Spectral Theory and Bezout Theorem

Juan Carlos Sampedro

Abstract

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

Spectral Theory and Bezout Theorem

Abstract

This note investigates the hidden relationship between the concept of algebraic multiplicity of an eigenvalue and the local intersection index of algebraic varieties.
Paper Structure (4 sections, 7 theorems, 57 equations)

This paper contains 4 sections, 7 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. Results for admissible curves
  3. Results in the general case
  4. Worked example

Key Result

Lemma 2.1

Let $L\in \mathcal{A}(k^{n})$ and $\lambda_{0}\in k$. Then, the following ideal identity holds

Theorems & Definitions (12)

  • Definition 2.1
  • Lemma 2.1
  • proof
  • Theorem 2.1
  • proof
  • Corollary 2.1
  • Theorem 2.2
  • proof
  • Corollary 2.2
  • Theorem 3.1
  • ...and 2 more