U-Invariants for forms of higher degree

TL;DR

This paper introduces generalized u-invariants for higher degree forms, extending the classical quadratic form invariant, and compiles existing and new results related to these invariants.

Contribution

It defines both general and diagonal u-invariants for higher degree forms, broadening the scope of classical quadratic form invariants.

Findings

Collection of old and new results on these invariants

Extension of u-invariant concepts to higher degree forms

Framework for analyzing forms of higher degree

Abstract

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.