On projective degenerations of Veronese spaces

Here we give several examples of projective degenerations of subvarieties of ${\displaystyle {\mathbb{P}}^t}$. The more important case considered here is the d-ple Veronese embedding of ${\displaystyle {\mathbb{P}}^n}$; we will show how to degenerate it to the union of ${\displaystyle d^n}$ n-dimensional linear subspaces of ${\displaystyle {\mathbb{P}}^t;t:=\frac{n+d}{n!d!}-1}$ and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to postulation problems and to embedding problems.