Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On varieties as hyperplane sections
HTML articles powered by AMS MathViewer

by E. Ballico PDF
Proc. Amer. Math. Soc. 120 (1994), 405-411 Request permission

Abstract:

Here we extend to the the singular (but locally complete intersection) case a theorem of L’vovsky giving a condition ("${h^0}({N_X}( - 1)) \leqslant n + 1$") forcing a variety $X \subset {{\mathbf {P}}^n}$ not to be a hyperplane section (except of cones). Then we give a partial extension of this criterion to the case of subvarieties of a Grassmannian.
References
  • Edoardo Ballico, On singular curves in the case of positive characteristic, Math. Nachr. 141 (1989), 267–273. MR 1014431, DOI 10.1002/mana.19891410124
  • Open problems, Algebraic curves and projective geometry (Trento, 1988) Lecture Notes in Math., vol. 1389, Springer, Berlin, 1989, pp. 276–285. Collected by E. Ballico and C. Ciliberto. MR 1023406, DOI 10.1007/BFb0085940
    • J. O. Kleppe, The Hilbert-flag scheme, its properties and its connection with the Hilbert scheme. Applications to curves in $3$-space, Thesis, Oslo, 1981.
  • Jan O. Kleppe, Nonreduced components of the Hilbert scheme of smooth space curves, Space curves (Rocca di Papa, 1985) Lecture Notes in Math., vol. 1266, Springer, Berlin, 1987, pp. 181–207. MR 908714, DOI 10.1007/BFb0078184
    • —, Liaison of families of subschemes in ${{\mathbf {P}}^n}$, Algebraic Curves and Projective Geometry, Lecture Notes in Math., vol. 1389, Springer-Verlag, New York, 1989, pp. 128-173.
  • Dan Laksov, Indecomposability of restricted tangent bundles, Young tableaux and Schur functors in algebra and geometry (Toruń, 1980), Astérisque, vol. 87, Soc. Math. France, Paris, 1981, pp. 207–219. MR 646821
    • S. L’vovsky, Extensions of projective varieties and deformations, preprint. D. Perrin, Courbes passant par $m$ points généraux de ${{\mathbf {P}}^3}$, Memoire 28/29 (Nouvelle série), supplement to Bull. Soc. Math. France 115 (1987).
  • J. M. Wahl, A cohomological characterization of $\textbf {P}^{n}$, Invent. Math. 72 (1983), no. 2, 315–322. MR 700774, DOI 10.1007/BF01389326
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14N05, 14M10
  • Retrieve articles in all journals with MSC: 14N05, 14M10
Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 120 (1994), 405-411
  • MSC: Primary 14N05; Secondary 14M10
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1172946-8
  • MathSciNet review: 1172946