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

Abstract

For any algebraic scheme $X$ and every $(n,\mathcal{L})\in \mathbb{Z}\times \text{Pic}(X)$ we define an associated involution of its Chow group $A_{\ast }X$, 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.