# On projective degenerations of Veronese spaces

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 45-51
- ISSN: 0137-6934

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topBallico, Edoardo. "On projective degenerations of Veronese spaces." Banach Center Publications 37.1 (1996): 45-51. <http://eudml.org/doc/208615>.

@article{Ballico1996,

abstract = {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.},

author = {Ballico, Edoardo},

journal = {Banach Center Publications},

keywords = {degeneration; Hilbert scheme; Veronese embedding},

language = {eng},

number = {1},

pages = {45-51},

title = {On projective degenerations of Veronese spaces},

url = {http://eudml.org/doc/208615},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Ballico, Edoardo

TI - On projective degenerations of Veronese spaces

JO - Banach Center Publications

PY - 1996

VL - 37

IS - 1

SP - 45

EP - 51

AB - 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.

LA - eng

KW - degeneration; Hilbert scheme; Veronese embedding

UR - http://eudml.org/doc/208615

ER -

## References

top- [1] E. Ballico and Ph. Ellia, On projections of ruled and Veronese surfaces, J. Algebra 121 (1989), 477-487. Zbl0675.14015
- [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. Zbl0815.14023
- [5] A. Van de Ven, On uniform vector bundles, Math. Ann. 195 (1978), 245-248.

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