On projective degenerations of Veronese spaces

• Autorzy: Edoardo Ballico
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 45-51

Daty

wydano

1996

Twórcy

autor

Edoardo Ballico

• Department of Mathematics, University of Trento, I-38050 Povo (TN), Italy

Bibliografia

• [1] E. Ballico and Ph. Ellia, On projections of ruled and Veronese surfaces, J. Algebra 121 (1989), 477-487.
• [2] M. Maruyama, Elementary transformations of algebraic vector bundles, in: Algebraic Geometry - Proceedings La Rabida, 241-266, Lect. Notes in Math. 961, Springer-Verlag, 1983.
• [3] B. Moishezon, Algebraic surfaces and the arithmetic of braids, II, in: Algebra and geometry, papers in honor of I. Shafarevich, vol. II, 311-344, Contemporary Math. 44, 1985.
• [4] B. Moishezon and M. Teicher, Braid group techniques in complex geometry III: projective degeneration of $V_3$, in: Classification of Algebraic Varieties, 313-332, Contemporary Math. 162, 1994.
• [5] A. Van de Ven, On uniform vector bundles, Math. Ann. 195 (1978), 245-248.