Skip to main content
SpringerLink
Log in

Connectivity and its applications in algebraic geometry

  • Conference paper
  • First Online:
Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 862))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abhyankar, Tame coverings and fundamental groups of algebraic varieties I; II, Amer. J. Math. 81 (1959), 46–94; 82 (1960), 120–178.

    Article  MathSciNet  Google Scholar 

  2. D. Alibert and G. Maltsiniotis, Groupe fondamentale du complémentaire d'une courbe à points doubles ordinaires, Bull. Soc. Math. France 102 (1974), 335–51.

    MathSciNet  MATH  Google Scholar 

  3. E. Arbarello, M. Cornalba, P. Griffiths and J. Harris, Geometry of Algebraic Curves, Princeton University Press, to appear.

    Google Scholar 

  4. W. Barth, Verallgemeinerung des Bertinischen Theorems in Abelschen Mannigfaltigkeiten, Annali della Scuola Normale Superiore di Pisa 23 (1969), 317–330.

    MathSciNet  MATH  Google Scholar 

  5. W. Barth, Transplanting cohomology classes in complex projective space, Amer. J. Math. 92 (1970), 951–967.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. Barth, Larsen's theorem on the homotopy groups of projective manifolds of small embedding codimension, Proc. Symp. Pure Math. 29 (1975), 307–313.

    Article  MathSciNet  MATH  Google Scholar 

  7. W. Barth and M. E. Larsen, On the homotopy types of complex projective manifolds, Math. Scand. 30 (1972), 88–94.

    MathSciNet  MATH  Google Scholar 

  8. E. Bertini, Introduzione alla geometria proiettiva degli iperspazi, Enrico Spoerri, Pisa, 1907.

    MATH  Google Scholar 

  9. D. Cheniot, Une demonstration du théorème de Zariski sur les sections hyperplanes d'une hypersurface projective et du théorème de Van Kampen sur le groupe fondamental du complémentaire d'une courbe projective plane, Compositio Math 27 (1973), 141–158.

    MathSciNet  MATH  Google Scholar 

  10. P. Deligne, letter, July 3, 1979.

    Google Scholar 

  11. P. Deligne, Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien, Séminaire Bourbaki, no 543, Nov. 1979.

    Google Scholar 

  12. P. Deligne, letter, November 18, 1979.

    Google Scholar 

  13. P. Deligne and N. Katz, Groupes de monodromie en géometrie algébrique, Lecture Notes in Math. 340 (1973).

    Google Scholar 

  14. G. Faltings, Algebraisation of some formal vector-bundles, Annals of Math, 110 (1979) 501–514.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Faltings, Formale Geometrie und homogene Räume, preprint (Münster, 1980).

    Google Scholar 

  16. W. Fulton, On the fundamental group of the complement of a node curve, Annals of Math. 111 (1980), 407–409.

    Article  MathSciNet  MATH  Google Scholar 

  17. W. Fulton, Notes on connectivity in algebraic geometry, preprint (1979).

    Google Scholar 

  18. W. Fulton, Intersection theory, notes for C.N.S. summer school on Intersection theory and enumerative geometry, Cortona, Italy, 1980.

    Google Scholar 

  19. W. Fulton and J. Hansen, A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings, Annals of Math. 110 (1979), 159–166.

    Article  MathSciNet  MATH  Google Scholar 

  20. T. Gaffney and R. Lazarsfeld, On the ramification of branched coverings of pn, Inventiones Math. 59 (1980), 53–58.

    Article  MathSciNet  MATH  Google Scholar 

  21. O. Gerstner and L. Kaup, Homotopiegruppen von Hyperflächenshnitten, Math. Annalen 204 (1973), 105–130.

    Article  MathSciNet  MATH  Google Scholar 

  22. W-D. Geyer, Zahm verzweigte Überlagerungen mit orthosingulärem Verzweigungsort, Inventiones math. 15 (1972); 67–71.

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Goresky and R. MacPherson, Stratified Morse theory, preprint (January 1980).

    Google Scholar 

  24. P. Griffiths, Hermitian differential geometry, Chern classes, and positive vector bundles, in Global Analysis (papers in honor of K. Kodaira), Princeton University Press, Princeton N.J., 1969, 185–251.

    Google Scholar 

  25. P. Griffiths and J. Harris, Algebraic geometry and local differential geometry, Ann. Scient. Ec. Norm. Sup. 12 (1979), 355–432.

    MathSciNet  MATH  Google Scholar 

  26. A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, Séminaire de Géométrie Algébrique (1962), North Holland, 1968.

    Google Scholar 

  27. A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique, Publ. Math. IHES 4, 8, 11, 17, 20, 24, 28, 32, 1960–67.

    Google Scholar 

  28. R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, N.J., 1965.

    Google Scholar 

  29. H. Hamm, Lokale topologische Eigenschaften komplexer Räume, Math. Annalen 191 (1971) 235–252

    Article  MathSciNet  MATH  Google Scholar 

  30. H. Hamm, On the vanishing of local homotopy groups for isolated singularities of complex spaces, preprint, 1980.

    Google Scholar 

  31. H. A. Hamm and Lê Dũng Tráng, Un théorème de Zariski du type de Lefschetz, Ann. Scient. Éc. Norm. Sup. 6 (1973), 317–366.

    MATH  Google Scholar 

  32. J. Hansen, thesis, Brown University, Jan. 1980.

    Google Scholar 

  33. R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Math. 156, 1970.

    Google Scholar 

  34. R. Hartshorne, Varieties of small codimension in projective space, Bull. A.M.S. 80 (1974) 1017–1032.

    Article  MathSciNet  MATH  Google Scholar 

  35. R. Hartshorne and R. Speiser, Local cohomological dimension in characteristic p, Annals. of Math. 105 (1977), 45–79

    Article  MathSciNet  MATH  Google Scholar 

  36. H. Hironaka and H. Matsumura, Formal functions and formal embeddings, J. Math. Soc. Japan 20 (1968), 52–82.

    Article  MathSciNet  MATH  Google Scholar 

  37. A. Holme, On the dual of a smooth variety, in K. Lønsted, ed., Algebraic Geometry, Lecture Notes in Math. 732. (1979), 144–156.

    Google Scholar 

  38. K. Johnson, Immersion and embedding of projective varieties, Acta Math 140 (1978), 49–74.

    Article  MathSciNet  MATH  Google Scholar 

  39. J. P. Jouanolou, Théorèmes de Bertini et applications, Series de Mathématiques Pures et Appliquées, I.R.M.A. Strasbourg, 1979.

    Google Scholar 

  40. K. K. Karchyauskis, A generalized Lefschetz theorem, Functional Analysis and its Applications 11 (1977), 312–313.

    Article  MathSciNet  Google Scholar 

  41. M. Kato, Partial Poincaré duality for k-regular spaces and complex algebraic sets, Topology 16 (1977), 33–50.

    Article  MathSciNet  MATH  Google Scholar 

  42. S. Kleiman, The enumerative theory of singularities, in P. Holme, ed., Real and Complex Singularities, Oslo 1976, Sijthoff and Noordhoof, Alphen aan den Rijn, (1977), 297–396.

    Google Scholar 

  43. A. Landman, lectures at Aarhus university, June 1976 (unpublished)

    Google Scholar 

  44. M. Larsen, On the topology of complex projective manifolds, Inventiones Math. 19 (1973), 251–260.

    Article  MathSciNet  MATH  Google Scholar 

  45. R. Lazarsfeld, A Barth-type theorem for branched coverings of projective space, Math. Annalen 249 (1980), 153–162.

    Article  MathSciNet  MATH  Google Scholar 

  46. R. Lazarsfeld, thesis, Brown University, June 1980.

    Google Scholar 

  47. J. Milnor, Morse theory, Annals of Math. Studies No. 51, Princeton, (1963).

    Google Scholar 

  48. D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Grundlehren der mathematischen Wissenschaften 221, Springer-Verlag, Berlin, Heidelberg, New York, 1976.

    MATH  Google Scholar 

  49. D. Mumford, letter, July 4, 1978.

    Google Scholar 

  50. P. Newstead, Some subvarities of grassmannians of codimension 3, Bull. London Math. Soc. 12 (1980), 177–182.

    Google Scholar 

  51. P. Newstead, A note on the homology groups of varieties defined by s equations, Bull. London Math. Soc. 12 (1980), 183–186.

    Article  MathSciNet  MATH  Google Scholar 

  52. A. Ogus, Local cohomological dimension of algebraic varieties, Ann. of Math. 98 (1973), 327–366.

    Article  MathSciNet  MATH  Google Scholar 

  53. A. Ogus, On the formal neighborhood of a subvariety of projective space, Amer. J. Math. 97 (1975), 1085–1107.

    Article  MathSciNet  MATH  Google Scholar 

  54. M. Oka, On the fundamental group of the complement of a reducible curve in Pn, J. Lon. M. Soc. 12 (1976), 239–252.

    Article  MathSciNet  MATH  Google Scholar 

  55. D. Prill, The fundamental group of the complement of an algebraic curve, Manuscripta math 14 (1974), 163–172.

    Article  MathSciNet  MATH  Google Scholar 

  56. R. Randell, The fundamental group of the complement of a singular plane curve, Quart. J. Math. Oxford 31 (1980), 71–79.

    Article  MathSciNet  MATH  Google Scholar 

  57. J. Roberts, On Zak's proof of Hartshorne's conjecture on linear normality, preprint (1980).

    Google Scholar 

  58. H. Rossi, Continuation of subvarieties of projective varieties, Amer. J. Math 91 (1969), 565–575.

    Article  MathSciNet  MATH  Google Scholar 

  59. J. P. Serre, Revêtements ramifiés du plan projectif, Séminaire Bourbaki no 204, 1959/60.

    Google Scholar 

  60. A. Sommese, Submanifolds of abelian varieties, Math. Annalen 233 (1978), 229–256.

    Article  MathSciNet  MATH  Google Scholar 

  61. A. Sommese, Complex subspaces of homogeneous complex manifolds I. Transplanting theorems, Duke Math. J. 46 (1979), 527–548.

    Article  MathSciNet  MATH  Google Scholar 

  62. A. Sommese, Complex subspaces of homogeneous complex manifolds IV. Homotopy results (preprint)

    Google Scholar 

  63. A. Sommese, Concavity theorems II (preprint)

    Google Scholar 

  64. A. Terracini, Sulle Vk per cui la varieta degli Sh (h+1)-seganti ha dimensione minare dell'ordinario, Rend. Circ. Mat. Palermo (1) 31 (1911) 392–396.

    Article  MathSciNet  MATH  Google Scholar 

  65. F. L. Zak, letter, December 26, 1979.

    Google Scholar 

  66. O. Zariski, On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math. 51 (1929), 305–328.

    Article  MathSciNet  MATH  Google Scholar 

  67. O. Zariski, A theorem on the Poincaré group of an algebraic hypersurface, Annals of Math. 38 (1937), 131–141.

    Article  MathSciNet  MATH  Google Scholar 

  68. O. Zariski, Algebraic Surfaces, second supplemented edition, Ergebnisse der Math. und ihrer Grenzgebiete, Band 61, Springer-Verlag, New York, Heidelberg, Berlin, 1971.

    Book  MATH  Google Scholar 

  69. O. Zariski, Collected Papers, Part III, Topology of curves and surfaces and special topics in the theory of algebraic varieties, Mathematicians of Our Time Series, The MIT Press, Cambridge, Mass. and London, Eng., 1978.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Brown University, 02912, Providence, RI

    William Fulton & Robert Lazarsfeld

  2. Department of Mathematics, Harvard University, 02138, Cambridge, MA

    William Fulton & Robert Lazarsfeld

Authors
  1. William Fulton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Lazarsfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Anatoly Libgober Philip Wagreich

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Fulton, W., Lazarsfeld, R. (1981). Connectivity and its applications in algebraic geometry. In: Libgober, A., Wagreich, P. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090889

Download citation

  • DOI: https://doi.org/10.1007/BFb0090889

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10833-7

  • Online ISBN: 978-3-540-38720-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation