Skip to main content
SpringerLink
Log in

The Betti numbers of the Hilbert scheme of points on a smooth projective surface

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

References

  1. Beauville, A.: Variétés kählériennes dont la première classe de Chern est nulle. J. Diff. Geom.18, 755–782 (1983)

    MathSciNet  MATH  Google Scholar 

  2. Bialynicki-Birula, A.: Some theorems on actions of algebraic groups. Ann. Math.98, 480–497 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bialynick-Birula, A.: Some properties of the decompositions of algebraic varieties determined by actions of a torus. Bull. Acad. Pol. Sér. Sci. Math. astron. Phys.24, 667–674 (1976)

    MathSciNet  MATH  Google Scholar 

  4. Briançon, J.: Description de HilbnC{x, y}. Invent. Math.41, 45–89 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  5. Deligne, P.: la conjecture de Weil. I. Inst. Hautes Etudes Sci. Publ. Math.43, 273–307 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ellingsrud, G., Strømme, S.A.: On the homology of the Hilbert scheme of points in the plane. Invent. Math.87, 343–352 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fogarty, J.: Algebraic families on an algebraic surface. Am. J. Math.10, 511–521 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fogarty, J.: Algebraic families on an algebraic surface. II. Picard scheme of the punctual Hilbert scheme. Am. J. Math.96, 660–687 (1974)

    MathSciNet  MATH  Google Scholar 

  9. Fulton, W.: Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  10. Fujiki, A.: On primitive symplectic compact KählerV-manifolds of dimension four. Classification of algebraic and analytic manifolds (Katata 1981). Prog. Math. 59. Boston: Birkhäuser 1983

    Google Scholar 

  11. Göttsche, L.: Die Betti-Zahlen des Hilbert-Schemas für Unterschemata der Längen einer glatten Fläche. Diplomarbeit, Bonn, Juli 1988

  12. Grothendieck, A.: Techniques de construction et théorèmes d'existence en géometrie algébrique. IV. Les schémas de Hilbert. Sém. Bourbaki221 (1960/61)

  13. Hirschowitz, A.: Le groupe de Chow équivariant. C.R. Acad. Sci. Paris Sér. 1298, 87–89 (1984)

    MathSciNet  MATH  Google Scholar 

  14. Iarrobino, A.: Punctual Hilbert schemes. Mem. Am. Math. Soc.188 (1977)

  15. Iarrobino, A.: Punctual Hilbert schemes. Bull. Am. Math. Soc.78, 819–823 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  16. Iarrobino, A.: Hilbert scheme of points: overview of last ten years. Proc. of Symp. in Pure Math., Vol. 46, Part 2, Algebraic Geometry, Bowdoin 297–320 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  17. Macdonald, I.G.: The Poincaré polynomial of a symmetric product. Proc. Camb. Phil. Soc.58, 563–568 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mazur, B.: Eigenvalues of Frobenius acting on algebraic varieties over finite fields. Proc. of Symp. in Pure Math., Vol. 29, Algebraic Geometry, Arcata 231–261 (1974)

    Article  MathSciNet  Google Scholar 

  19. Milne, J.S.: Étale Cohomology. Princeton Math. Series 33. Princeton: Princeton University Press 1980

    MATH  Google Scholar 

  20. Grothendieck, A. et al.: Séminaire de Géometrie Algébrique 1: Revêtements étales et groupe fondamental (1960–61). (Lecture Notes in Math. 224). Berlin Heidelberg New York: Springer 1971

    MATH  Google Scholar 

  21. Steenbrink, J.H.M.: Mixed Hodge structures on the vanishing cohomology. Nordic Summer School, Symposium in Mathematics, Oslo 1970, 525–563. Alphen an den Rijn: Sijthoff and Noordhoff 1977

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, 46556, Notre Dame, IN, USA

    Lothar Göttsche

Authors
  1. Lothar Göttsche
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Hans Grauert

Rights and permissions

Reprints and permissions

About this article

Cite this article

Göttsche, L. The Betti numbers of the Hilbert scheme of points on a smooth projective surface. Math. Ann. 286, 193–207 (1990). https://doi.org/10.1007/BF01453572

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01453572

Keywords

Search

Navigation