Polysymmetric functions and motivic measures of configuration spaces

TL;DR

This paper introduces a generalized class of symmetric functions and uses this theory to compute motivic measures of configuration spaces, specifically the class of irreducible hypersurfaces in projective space, within the Grothendieck ring.

Contribution

It develops a new framework of polysymmetric functions and applies it to algebraic geometry problems involving motivic measures of configuration spaces.

Findings

Computed the class of irreducible hypersurfaces in the Grothendieck ring.

Established a connection between polysymmetric functions and motivic measures.

Provided new tools for studying configuration spaces in algebraic geometry.

Abstract

We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.