Skip to main content
Log in

On plurigenera of normal isolated singularities. I

  • 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

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

Instant access to the full article PDF.

References

  1. Arnold, V.: Normal forms for functions near degenerate critical points, the Weyl groupA k ,D k ,E k and Lagrangian singularities. Functional Anal. App.6, 254–272 (1972)

    Google Scholar 

  2. Artin, E.: On isolated rational singularities of surfaces. Amer. J. Math.88, 129–136 (1966)

    Google Scholar 

  3. Brieskorn, E.: Rationale Singularitäten komplexer Flächen. Invent. Math.14, 336–358 (1968)

    Google Scholar 

  4. Burns, D.: On rational singularities in dimensions >2. Math. Ann.211, 237–244 (1974)

    Google Scholar 

  5. Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331–368 (1962)

    Google Scholar 

  6. Higuchi, T., Watanabe, K., Ohyanagi, S.: On purely elliptic singularities. Sci. Rep. Yokohama Nat. Univ. Sect. I25, 33–35 (1978)

    Google Scholar 

  7. Hironaka, H.: Bimeromorphic smoothing of complex spaces. In: Lecture Notes. Harvard University 1971

  8. Hirzebruch, F.: Hilbert modular surfaces. Enseignement Math.19, 183–281 (1973)

    Google Scholar 

  9. Karras, U.: Klassifikationen zweidimensionaler Singularitäten mit auflösbaren lokalen Fundamentalgruppen. Math. Ann.213, 231–255 (1975)

    Google Scholar 

  10. Kato, M.: Riemann-Roch theorem for strongly pseudoconvex manifolds of dimension 2. Math. Ann.222, 243–250 (1976)

    Google Scholar 

  11. Knöller, F.W.: 2-dimensionale Singularitäten und Differentialformen. Math. Ann.206, 205–213 (1973)

    Google Scholar 

  12. Laufer, H.B.: Normal two-dimensional singularities. Princeton: Princeton University Press 1971

    Google Scholar 

  13. Laufer, H.B.: On rational singularities. Amer. J. Math.94, 597–608 (1972)

    Google Scholar 

  14. Laufer, H.B.: Taut two-dimensional singularities. Math. Ann.205, 131–164 (1973)

    Google Scholar 

  15. Laufer, H.B.: On minimally elliptic singularities. Amer. J. Math.99, 1257–1295 (1977)

    Google Scholar 

  16. Morrow, J., Kodaira, K.: Complex manifolds. New York: Holt, Rinehard & Winston 1971

    Google Scholar 

  17. Pinkham, H.: Normal surface singularities withC* action. Math. Ann.227, 183–193 (1977)

    Google Scholar 

  18. Saito, K.: Einfach-elliptische Singularitäten. Invent. Math.23, 289–325 (1974)

    Google Scholar 

  19. Sakai, F.: Kodaira dimensions of complements of divisors. Complex analysis and algebraic geometry: a collection of papers dedicated to K. Kodaira. Tokyo: Iwanami 1977

    Google Scholar 

  20. Siu, T.: Absolute gap-sheaves and extension of coherent analytic sheaves. Trans. Amer. Math. Soc.141, 361–376 (1969)

    Google Scholar 

  21. Tomaru, T.: Plurigenera δ m for 2-dimensional normal singularities withC*-action. Preprint 1979

  22. Ueno, K.: Classification theory of algebraic varieties and compact complex spaces. In: Lectures Notes in Mathematics 439. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

  23. Wagreich, P.: Singularities of complex surfaces with solvable local fundamental group. Topology11, 51–72 (1972)

    Google Scholar 

  24. Wagreich, P.: Elliptic singularities of surfaces. Amer. J. Math.92, 419–454 (1970)

    Google Scholar 

  25. Watanabe, K.: Two dimensional quotient singularities and integrable differential forms. 1978 (unpublished)

  26. Watanabe, K.: On purely elliptic singularties of dimensions >2. 1979 (in preparation)

  27. Yau, S.S.T.: Two theorems in higher dimensional singularities. Math. Ann.231, 44–59 (1977)

    Google Scholar 

  28. Yoshinaga, E., Ohyanagi, S.: A criterion for 2-dimensional normal singularities to be weakly elliptic. Sci. Rep. Yokohama Nat. Univ. (to appear)

  29. Yoshinaga, E., Watanabe, K.: On the geometric genus and the inner modality of quasihomogeneous isolated singularities. Sci. Rep. Yokohama Nat. Univ. Sect. I25, 45–53 (1978)

    Google Scholar 

  30. Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math. I.H.E.S.36 (1969)

  31. Andreotti, A., Grauert, H.: Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. France90, 193–259 (1962)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watanabe, K. On plurigenera of normal isolated singularities. I. Math. Ann. 250, 65–94 (1980). https://doi.org/10.1007/BF01422185

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01422185

Navigation