On projective degenerations of Veronese spaces

Volume 37 / 1996

Edoardo Ballico Banach Center Publications 37 (1996), 45-51 DOI: 10.4064/-37-1-45-51


Here we give several examples of projective degenerations of subvarieties of $ℙ^{t}$. The more important case considered here is the d-ple Veronese embedding of $ℙ^{n}$; we will show how to degenerate it to the union of $d^{n}$ n-dimensional linear subspaces of $ℙ^{t}; t:= (n+d)/(n!d!) - 1$ 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.


  • Edoardo Ballico

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