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Mathematics of the USSR-Sbornik, 1983, Volume 44, Issue 4, Pages 535–544
DOI: https://doi.org/10.1070/SM1983v044n04ABEH000986 (Mi sm2488) 		 
This article is cited in 39 scientific papers (total in 39 papers)

Projections of algebraic varieties

F. L. Zak
English version PDF (695 kB) Citations (39) Russian version article
References:
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DOI: https://doi.org/10.1070/SM1983v044n04ABEH000986
Abstract: This paper gives conditions which are necessary and sufficient in order that a generic projection of a projective variety not have singularities other than those coming from the singularities of the original variety. In particular it turns out that this is possible only for varieties of large codimension.
Bibliography: 5 titles.
Received: 17.12.1980
Bibliographic databases:
UDC: 513.6
MSC: Primary 14E22, 14E25, 14N05; Secondary 14M07, 51N35
Language: English
Original paper language: Russian
Citation: F. L. Zak, “Projections of algebraic varieties”, Math. USSR-Sb., 44:4 (1983), 535–544
Citation in format AMSBIB
\Bibitem{Zak81}
\by F.~L.~Zak
\paper Projections of algebraic varieties
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 4
\pages 535--544
\mathnet{http://mi.mathnet.ru/eng/sm2488}
\crossref{https://doi.org/10.1070/SM1983v044n04ABEH000986}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=665860}
\zmath{https://zbmath.org/?q=an:0511.14026|0484.14016}
Linking options:
  • https://www.mathnet.ru/eng/sm2488
  • https://doi.org/10.1070/SM1983v044n04ABEH000986
  • https://www.mathnet.ru/eng/sm/v158/i4/p593
    • This publication is cited in the following 39 articles:
    1. Izv. Math., 88:3 (2024), 419–467  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Junho Choe, Sijong Kwak, “A matryoshka structure of higher secant varieties and the generalized Bronowski's conjecture”, Advances in Mathematics, 406 (2022), 108526  crossref
    3. Remke Kloosterman, Sławomir Rams, “Quintic threefolds with triple points”, Commun. Contemp. Math., 23:01 (2021), 1950085  crossref
    4. Carlos Sierra J., “A Remark on Zak'S Theorem on Tangencies”, Math. Res. Lett., 18:4 (2011), 783–789  crossref  mathscinet  zmath  isi
    5. Chiantini L., Ciliberto C., “On the Dimension of Secant Varieties”, J. Eur. Math. Soc., 12:5 (2010), 1267–1291  crossref  mathscinet  zmath  isi
    6. Carlos Sierra J., “Smooth N-Dimensional Subvarieties of P2N-1 Containing a Family of Very Degenerate Divisors”, Int. J. Math., 20:1 (2009), 109–122  crossref  mathscinet  zmath  isi
    7. F. Laytimi, D. S. Nagaraj, “Barth type vanishing theorem”, Geom Dedicata, 2008  crossref  mathscinet  isi
    8. Bogomolov F., De Oliveira B., “Symmetric Tensors and Geometry of P-N Subvarieties”, Geom. Funct. Anal., 18:3 (2008), 637–656  crossref  mathscinet  zmath  isi
    9. Mezzetti E., Tommasi O., “Some Remarks on Varieties with Degenerate Gauss Image”, Pac. J. Math., 213:1 (2004), 79–88  crossref  mathscinet  zmath  isi
    10. Angelo Felice Lopez, Ziv Ran, “On the irreducibility of secant cones, and an application to linear normality”, Duke Math. J., 117:3 (2003)  crossref
    11. Kachi Y. Sato E., “Segre's Reflexivity and an Inductive Characterization of Hyperquadrics - Introduction”, Mem. Am. Math. Soc., 160:763 (2002), 1+  mathscinet  isi
    12. Ellia P., Franco D., “On Codimension Two Subvarieties of P-5 and P-6”, J. Algebr. Geom., 11:3 (2002), 513–533  crossref  mathscinet  zmath  isi
    13. Simis A., Ulrich B., Vasconcelos W., “Tangent Star Cones”, J. Reine Angew. Math., 483 (1997), 23–59  mathscinet  zmath  isi
    14. Amerik E., “On Codimension-Two Subvarieties of Hypersurfaces”, J. Reine Angew. Math., 483 (1997), 61–73  mathscinet  zmath  isi
    15. Flenner H., Vogel W., “Joins, Tangencies and Intersections”, Math. Ann., 302:3 (1995), 489–505  crossref  mathscinet  zmath  isi
    16. The Adjunction Theory of Complex Projective Varieties, 1995, 355  crossref
    17. Christian Okonek, “Notes on varieties of codimension 3 in ℙ N”, manuscripta math, 84:1 (1994), 421  crossref  mathscinet  zmath
    18. Luo Z., Tsitsiklis J., “On the Communication Complexity of Distributed Algebraic Computation”, J. ACM, 40:5 (1993), 1019–1047  crossref  mathscinet  zmath  isi
    19. Alzati A., “Barth Type Vanishing Theorems”, Geod. Dedic., 44:2 (1992), 159–168  mathscinet  zmath  isi
    20. Ballico E., “On Projective Varieties with Projectively Equivalent Zero-Dimensional Linear Sections”, Can. Math. Bul.-Bul. Can. Math., 35:1 (1992), 3–13  crossref  mathscinet  zmath  isi
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