On certain hypersurfaces with non-isolated singularities in $\mathrm {P}^4(\mathbf {C})$

Abstract

We give an example of hypersurfaces with non-isolated singularities in $\mathrm{P}^4(\mathbf{C})$, whose normalizations have isolated rational quadruple points only as singularities. From Schlessinger's criterion, it follows that these isolated rational singular points are rigid under small deformations.