An algebro-geometric model for the configuration category

TL;DR

This paper introduces an algebro-geometric model for the configuration category of smooth algebraic varieties using log-geometry, and demonstrates the formality of specific configuration spaces.

Contribution

It develops a novel algebraic geometric framework for configuration categories and proves their formality, advancing the understanding of their structure.

Findings

Constructed a log-geometry based model for configuration categories

Proved the formality of certain configuration spaces

Provides new tools for studying algebraic and topological properties

Abstract

Using log-geometry, we construct a model for the configuration category of a smooth algebraic variety. As an application, we prove the formality of certain configuration spaces.