On singularities of generic projection hypersurfaces

Abstract

The present work studies singularities of hypersurfaces arising from generic projections of smooth projective varieties, in the context of Du Bois and semi log canonical singularities. It is demonstrated that Du Bois singularities are semi log canonical under certain reasonable assumptions, and that products of Du Bois singularities are also Du Bois. We then proceed to demonstrate that low-dimensional generic projection hypersurfaces are Du Bois, but general ones are not.