Free factorization algebras and homology of configuration spaces in algebraic geometry

TL;DR

This paper constructs free factorization algebras in algebraic geometry and connects their factorization homology to the homology of configuration spaces, providing a new algebraic proof of homological stability.

Contribution

It introduces a method to build free factorization algebras in algebraic geometry and links them to configuration space homology, offering a novel algebraic approach.

Findings

Establishes a link between factorization homology and configuration space homology.

Provides an algebraic proof of homological stability for configuration spaces.

Develops a construction of free factorization algebras in algebraic geometry.

Abstract

We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an application, this construction allows for a purely algebro-geometric proof of homological stability of configuration spaces.