Advertisement

On the local torelli theorem, a review of known results

  • Chris Peters
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 683)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ahlfors, L.: Lectures on Quasiconformal mappings, Vannostrand Math. Studies # 10 (1964).Google Scholar
  2. [2]
    Griffiths, P.: Periods of integrals on algebraic manifolds I, II, Am. I. Math. 90 (1968) pp. 366–446, resp. 805–865.Google Scholar
  3. [3]
    Grauert, H.:Deformationen kompakter komplexer Räume, in: "Classifications of Algebraic Varieties and Compact Complex Manifolds", Springer Lecture Notes in Math. # 412. p 70–74.Google Scholar
  4. [4]
    Gunning, R.C.: Lectures on Riemann Surfaces, — idem —, Jacobi varieties, Math. Notes, Princeton Univ. Press # 2 (1966), # 12 (1974).Google Scholar
  5. [5]
    Hodge, W.V.D.: The theory and applications of harmonic integrals, Cambridge University Press (1959).Google Scholar
  6. [6]
    Kii, K.I.: A local Torelli theorem for cyclic coverings of ℙn with a positive canonical class. Math. U.S.S.R. Sbornik, 21 (1973), pp. 145–155 (transl. in 1974).MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Kodaira K. and Spencer D.: On deformations of complex analytic structures I, II, Ann. Math. 67 (1958), 328–466.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Kodaira, K. and Morrow, J.: Complex Manifolds, Holt-Rinehardt & Winston, New York (1971).zbMATHGoogle Scholar
  9. [9]
    Kuranishi, M.: On the locally complete families of complex analytic structures, Ann. of Math. 75 (1962) pp. 536–577.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Lieberman, D., Wilsker. R., Peters, C.: A Theorem of Local-Torelli Type. Math. Ann 2.... (1977).Google Scholar
  11. [11]
    Noether, M.: Uber invariante Darstellung algebraischer Funktionen, Math. Ann. 17 (1880), 263–284.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Peters, C.: The local Torelli theorem I, Math. Ann. 217, 146 (1975), Erratum Math. Ann 191–192 (1976), — idem — II, Ann. Sc. Norm. Pisa, Ser. IV, 3, 321–340 (1976).Google Scholar
  13. [13]
    Peters, C.: On Two Types of Surfaces of General Type with Vanishing Geometric Genus, Inv. Math. 32, 33–47 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Saint-Donat, B.: On Petri's Analysis of the Linear System of Quadrics through a Canonical Curve. Math. Ann. 206, 157–175 (1963).MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Torelli, R.: Sulle varietà di Jacobi, Rend. Accad. Lincei 22 (1914), 98–103.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Chris Peters
    • 1
  1. 1.Rijkuniversiteit LeidenMathematisches InstituutLeidenThe Netherlands

Personalised recommendations