Paper 2021/1611

Solving degree, last fall degree, and related invariants

Alessio Caminata and Elisa Gorla

Abstract

In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of solving a system of polynomial equations via Groebner bases methods. Our main results include a connection between the solving degree and the last fall degree and one between the degree of regularity and the Castelnuovo--Mumford regularity.