A configuration space model for algebraic function spaces

TL;DR

This paper introduces a configuration space model for algebraic maps between smooth projective varieties, providing an algebraic analogue of a topological result and extending the understanding of algebraic function spaces.

Contribution

It establishes a configuration space model for algebraic maps, offering a higher-dimensional analogue of existing topological results in algebraic geometry.

Findings

Configuration space model for algebraic maps proved

Analogue of Bendersky-Gitler's topological result established

Extends to higher dimensions in algebraic geometry

Abstract

We prove that the space of algebraic maps between two smooth projective varieties, under certain conditions, admit a configuration space model, thereby obtaining an algebro-geometric analogue of Bendersky-Gitler's result on topological function spaces. Our result is a natural higher dimensional counterpart of \cite[Theorem 3]{Ban24}.