Skip to main content
SpringerLink
Log in

Projective manifolds with the same homology as ℙk

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

Complex projective threefolds having the same integral homology groups as ℙ3 are classified. This classification is used to improve a result of Fujita on manifolds whose integral cohomology ring is the same as that of ℙk and applies to the problem of classifying polarized manifolds (X, A), A being a nonsingular hypersurface such thatH i (A, ℤ)≃H i (X, ℤ) fori≦2 dimA.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Artin, M., Mumford, D.: Some elementary examples of unirational varieties which are not rational. Proc. London Math. Soc. (3)25, 75–95 (1972).

    Google Scholar 

  2. Bindschadler, D., Brenton, L.: On singular 4-manifolds of the homology type of ℂℙ2. J. Math. Kyoto Univ.24, 67–81 (1984).

    Google Scholar 

  3. Fujita, T.: On topological characterization of complex projective spaces and affine linear spaces. Proc. Japan Acad.56A, 231–234 (1980).

    Google Scholar 

  4. Fujita, T.: On the structure of polarized manifolds with total deficiency one, III. J. Math. Soc. Japan.36, 75–89 (1984).

    Google Scholar 

  5. Griffiths, P. A.: Some results on algebraic cycles on algebraic manifolds. In: Algebraic Geometry. Bombay Colloquium 1968, pp. 93–191. Oxford: Univ. Press. 1969.

    Google Scholar 

  6. Iskowskih, V. A., Shokurov, V. V.: Biregular theory of Fano 3-folds. In: Algebraic Geometry (K. Lønsted, ed.). Copenhagen 1978, pp. 171–182. Lect. Notes Math.732. Berlin-Heidelberg-New York: Springer. 1979.

    Google Scholar 

  7. Mukai, S., Umemura, H.: Minimal rational threefolds. In: Algebraic Geometry (M. Raynaud and T. Shioda, eds.), Proc. Tokyo-Kyoto 1982, pp. 490–518. Lect. Notes Math.1016. Berlin-Heidelberg-New York: Springer. 1983.

    Google Scholar 

  8. Mumford, D.: An algebraic surface withK ample, (K 2)=9,p g =q=0. Amer. J. Math.101, 233–244 (1979).

    Google Scholar 

  9. Ueno, K.: Classification theory of algebraic varieties and compact complex spaces. Lect. Notes Math.439. Berlin-Heidelberg-New York: Springer. 1975.

    Google Scholar 

  10. Ueno, K.: Birational geometry of algebraic threefolds. In: Journées de Géométrie algébrique d'Angers 1979 (A. Beauville, ed.), pp. 311–322. Alphen: Sijthoff Noordhoff. 1980.

    Google Scholar 

  11. Yau, S. T.: Calabi's conjecture and some new results in algebraic geometry. Proc. Natl. Acad. Sci. U.S.A.74, 1798–1799 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica “F. Enriques”, Università di Milano, Via C. Saldini, 50, I-20133, Milano, Italy

    A. Lanteri

  2. Scuola Normale Superiore, Piazza dei Cavalieri, 7, I-56100, Pisa, Italy

    D. Struppa

Authors
  1. A. Lanteri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Struppa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by M.P.I. of the Italian Government. Both authors are members of G.N.S.A.G.A. of the Italian C.N.R.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lanteri, A., Struppa, D. Projective manifolds with the same homology as ℙk . Monatshefte für Mathematik 101, 53–58 (1986). https://doi.org/10.1007/BF01326846

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01326846

Keywords

Search

Navigation