On characteristic classes of singular hypersurfaces and involutive symmetries of the Chow group

TL;DR

This paper introduces involutions on the Chow group of algebraic schemes, showing they interchange characteristic classes of singular hypersurfaces, and demonstrates their realization via involutive correspondences in projective space.

Contribution

It defines new involutions on Chow groups linked to algebraic schemes and proves their effect on characteristic classes of singular hypersurfaces, including explicit realizations in projective space.

Findings

Involutions interchange characteristic classes of singular hypersurfaces.

Involutions are induced by correspondences in projective space.

The framework applies to algebraic schemes with line bundles.

Abstract

For any algebraic scheme $X$ and every $(n,\mathscr{L})\in \mathbb{Z}\times \text{Pic}(X)$ we define an associated involution of its Chow group $A_*X$, and show that certain characteristic classes of (possibly singular) hypersurfaces in a smooth variety are interchanged via these involutions. For $X=\mathbb{P}^N$ we show that such involutions are induced by involutive correspondences.