The Linearized System for Isometric Embeddings and Its Characteristic Variety

TL;DR

This paper proves that the characteristic variety of the isometric embedding system is not smooth in dimensions greater than 4, using a linearized system to analyze its properties.

Contribution

It introduces a smaller, equivalent linearized system to analyze the characteristic variety, confirming a conjecture about its non-smoothness in higher dimensions.

Findings

Characteristic variety is not smooth for dimensions > 4

Introduces a linearized system for analysis

Confirms conjecture by Bryant, Griffiths, and Yang

Abstract

In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension greater than 4. This is accomplished by introducing a smaller yet equivalent linearized system, in an appropriate way, which facilitates analysis of the characteristic variety.