Skip to main content
SpringerLink
Log in

Mordell-Weil lattices of type E8 and deformation of singularities

  • Conference paper
  • First Online:
Prospects in Complex Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1468))

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. Bourbaki, N.: Groupes et Algèbres de Lie, Chap. 4, 5 et 6, Hermann, Paris (1968).

    MATH  Google Scholar 

  2. Brieskorn, E.: Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen, Math. Ann. 166, 76–102 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  3. Brieskorn, E.: Die Auflösung der rationalen Singularitäten holomorpher Abbildungen, Math. Ann. 178, 255–270 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  4. Conway, J., Sloane, N.: Sphere Packings, Lattices and Groups, Grund. Math. Wiss. 290, Springer-Verlag (1988).

    Google Scholar 

  5. Demazure, M., Pinkham, H., Teissier, B.: Séminaire sur les Singularités des Surfaces, Lect. Notes in Math. 777 (1980).

    Google Scholar 

  6. Kodaira, K.: On compact analytic surfaces II–III, Ann. of Math. 77, 563–626 (1963); 78, 1–40(1963); Collected Works, vol.III, Iwanami and Princeton Univ. Press, 1269–1372 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  7. Looijenga, E.: On the semi-universal deformation of a simple-elliptic hypersurface singularity II:the discriminant, Topology 17, 23–40 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  8. Néron, A.: Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. I.H.E.S. 21(1964).

    Google Scholar 

  9. Oda, T.: Introduction to algebraic singularities, (to appear).

    Google Scholar 

  10. Oguiso, K., Shioda, T.: The Mordell-Weil lattice of a rational elliptic surface, (in preparation).

    Google Scholar 

  11. Pinkham, H.: Résolution simultanée de points doubles rationelles, in: [DPT], 179–2013 (1980).

    Google Scholar 

  12. Saito, K.: Algebraic surfaces for regular systems of weights, in: Algebraic Geometry and Commutative Algebra, vol.II, Kinokuniya, Tokyo, 517–612 (1988).

    Chapter  Google Scholar 

  13. Shioda, T.: Mordell-Weil lattices and Galois representation, I, II, III, Proc. Japan Acad. 65A, 267–271, 296–299, 300–303 (1989).

    MathSciNet  MATH  Google Scholar 

  14. Shioda, T.: Construction of elliptic curves with high rank via the invariants of the Weyl groups, (in preparation).

    Google Scholar 

  15. Slodowy, P.: Simple singularities and simple algebraic groups, Lect. Notes in Math. 815 (1980).

    Google Scholar 

  16. Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil, Lect. Notes in Math. 476, 33–52 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  17. Weil, A.: Foundation of Algebraic Geometry, AMS (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rikkyo University, Tokyo

    Tetsuji Shioda

Authors
  1. Tetsuji Shioda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Junjiro Noguchi Takeo Ohsawa

Additional information

Dedicated to Professor F. Hirzebruch

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Shioda, T. (1991). Mordell-Weil lattices of type E8 and deformation of singularities. In: Noguchi, J., Ohsawa, T. (eds) Prospects in Complex Geometry. Lecture Notes in Mathematics, vol 1468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086194

Download citation

  • DOI: https://doi.org/10.1007/BFb0086194

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54053-3

  • Online ISBN: 978-3-540-47370-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation