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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 4(12), Pages 593–602 (Mi msb2488)  

This article is cited in 33 scientific papers (total in 33 papers)

Projections of algebraic varieties

F. L. Zak


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.

Full text: PDF file (1083 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1983, 44:4, 535–544

Bibliographic databases:

UDC: 513.6
MSC: Primary 14E22, 14E25, 14N05; Secondary 14M07, 51N35
Received: 17.12.1980

Citation: F. L. Zak, “Projections of algebraic varieties”, Mat. Sb. (N.S.), 116(158):4(12) (1981), 593–602; Math. USSR-Sb., 44:4 (1983), 535–544

Citation in format AMSBIB
\Bibitem{Zak81}
\by F.~L.~Zak
\paper Projections of algebraic varieties
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 4(12)
\pages 593--602
\mathnet{http://mi.mathnet.ru/msb2488}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=665860}
\zmath{https://zbmath.org/?q=an:0511.14026|0484.14016}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 4
\pages 535--544
\crossref{https://doi.org/10.1070/SM1983v044n04ABEH000986}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Lazarsfeld R., “Some Applications of the Theory of Positive Vector-Bundles”, Lect. Notes Math., 1092 (1984), 29–61  crossref  mathscinet  zmath  isi
    2. F. L. Zak, “Severi varieties”, Math. USSR-Sb., 54:1 (1986), 113–127  mathnet  crossref  mathscinet  zmath
    3. F. L. Zak, “Linear systems of hyperplane sections on varieties of low codimension”, Funct. Anal. Appl., 19:3 (1985), 165–173  mathnet  crossref  mathscinet  zmath  isi
    4. Ein L., “Varieties with Small Dual Varieties .2.”, Duke Math. J., 52:4 (1985), 895–907  crossref  mathscinet  zmath  adsnasa  isi
    5. Dale M., “Severis Theorem on the Veronese-Surface”, J. Lond. Math. Soc.-Second Ser., 32:Part 3 (1985), 419–425  crossref  mathscinet  zmath  isi
    6. Holme A., Schneider M., “A Computer-Aided Approach to Codimension-2 Subvarieties of Pn, N-Greater-Than-Or-Equal-to-6”, J. Reine Angew. Math., 357 (1985), 205–220  mathscinet  zmath  isi
    7. Lawrence Ein, “Varieties with small dual varieties, I”, Invent math, 86:1 (1986), 63  crossref  mathscinet  zmath  isi
    8. Jennings G., “Lines Having High Contact with a Projective Variety”, Pac. J. Math., 125:1 (1986), 103–115  crossref  mathscinet  zmath  isi
    9. Pinkham H., “A Castelnuovo Bound for Smooth Surfaces”, Invent. Math., 83:2 (1986), 321–332  crossref  mathscinet  zmath  isi
    10. F. L. Zak, “Structure of Gauss maps”, Funct. Anal. Appl., 21:1 (1987), 32–41  mathnet  crossref  mathscinet  zmath  isi
    11. Peternell T., Lepotier J., Schneider M., “Vanishing Theorems, Linear and Quadratic Normality”, Invent. Math., 87:3 (1987), 573–586  crossref  mathscinet  zmath  isi
    12. Adlandsvik B., “Joins and Higher Secant Varieties”, Math. Scand., 61:2 (1987), 213–222  crossref  mathscinet  zmath  adsnasa  isi
    13. Fulton W., “On the Topology of Algebraic-Varieties”, Proc. Symp. Pure Math., 46:1 (1987), 15–46  crossref  mathscinet  zmath  isi
    14. Schneider M., “Vector-Bundles and Submanifolds of Projective-Space - 9 Open Problems”, Proc. Symp. Pure Math., 46:Part 2 (1987), 101–107  crossref  mathscinet  zmath  isi
    15. M. Andreatta, E. Ballico, “On the adjunction process over a surface in char.p”, manuscripta math, 62:2 (1988), 227  crossref  mathscinet  zmath  isi
    16. Fantechi B., “On the Superadditivity of Secant Defects”, Bull. Soc. Math. Fr., 118:1 (1990), 85–100  crossref  mathscinet  zmath  isi
    17. Alzati A., Ottaviani G., “A Linear Bound on the Tert-Normality of Codimension 2 Subvarieties of Pn”, J. Reine Angew. Math., 409 (1990), 35–40  mathscinet  zmath  isi
    18. Alzati A., “Barth Type Vanishing Theorems”, Geod. Dedic., 44:2 (1992), 159–168  mathscinet  zmath  isi
    19. 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
    20. Alzati A., “A New Castelnuovo Bound for 2 Codimensional Subvarieties of PR”, Proc. Amer. Math. Soc., 114:3 (1992), 607–611  crossref  mathscinet  zmath  isi
    21. Luo Z., Tsitsiklis J., “On the Communication Complexity of Distributed Algebraic Computation”, J. ACM, 40:5 (1993), 1019–1047  crossref  mathscinet  zmath  isi
    22. Christian Okonek, “Notes on varieties of codimension 3 in ℙ N”, manuscripta math, 84:1 (1994), 421  crossref  mathscinet  zmath
    23. Flenner H., Vogel W., “Joins, Tangencies and Intersections”, Math. Ann., 302:3 (1995), 489–505  crossref  mathscinet  zmath  isi
    24. Simis A., Ulrich B., Vasconcelos W., “Tangent Star Cones”, J. Reine Angew. Math., 483 (1997), 23–59  mathscinet  zmath  isi
    25. Amerik E., “On Codimension-Two Subvarieties of Hypersurfaces”, J. Reine Angew. Math., 483 (1997), 61–73  mathscinet  zmath  isi
    26. Kachi Y. Sato E., “Segre's Reflexivity and an Inductive Characterization of Hyperquadrics - Introduction”, Mem. Am. Math. Soc., 160:763 (2002), 1+  mathscinet  isi
    27. 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
    28. Mezzetti E., Tommasi O., “Some Remarks on Varieties with Degenerate Gauss Image”, Pac. J. Math., 213:1 (2004), 79–88  crossref  mathscinet  zmath  isi
    29. F. Laytimi, D. S. Nagaraj, “Barth type vanishing theorem”, Geom Dedicata, 2008  crossref  mathscinet  isi
    30. 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
    31. 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
    32. Chiantini L., Ciliberto C., “On the Dimension of Secant Varieties”, J. Eur. Math. Soc., 12:5 (2010), 1267–1291  crossref  mathscinet  zmath  isi
    33. Carlos Sierra J., “A Remark on Zak'S Theorem on Tangencies”, Math. Res. Lett., 18:4 (2011), 783–789  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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