Saito's theorem revisited and application to free pencils of hypersurfaces

Roberta Di Gennaro, Rosa Maria Miró-Roig

A hypersurface $X\subset {\mathbb{P}}^n$ is said to be free if its associated sheaf $T_X$ of vector fields tangent to $X$ is a free ${\mathcal{O}}_{{\mathbb{P}}^n}$-module. So far few exa…