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On deformations of quintic surfaces

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References

  1. Abhyanker, S.: Concepts of order and rank on a complex space and a condition for normality. Math. Ann.141, 171–192 (1960)

    Google Scholar 

  2. Akizuki, Y., Nakano, S.: Note on Kodaira-Spencer's proof of Lefschetz theorems. Proc. Japan Acad.30, 266–272 (1954)

    Google Scholar 

  3. Artin, M.: Some numerical criteria for contractibility of curves on an algebraic surface. Amer. J. Math.84, 485–496 (1962)

    Google Scholar 

  4. Bombieri, E.: Canonical models of surfaces of general type. Publ. Math. IHES42, 171–219 (1973)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  7. Enriques, F.: Le superficie algebriche. Bologna 1949

  8. Fujiki, A, Nakano, S.: Supplement to “On the inverse of monoidal transformation”. Publ. RIMS7, 637–644 (1971/72)

    Google Scholar 

  9. Grauert, H.: Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen. Publ. Math. IHES5 (1960)

  10. Grothendieck, A.: Techniques de construction en géométrie analytique. Séminaire H. Cartan13 (1960/61)

  11. Horikawa, E.: On deformations of holomorphic maps. I. J. Math. Soc. Japan25, 372–396 (1973). ibid. Horikawa, E.: On deformations of holomorphic maps. II. J. Math. Soc. Japan26, 647–667 (1974) III. to appear

    Google Scholar 

  12. Horikawa, E.: On deformations of quintic surfaces. Proc. Japan. Acad.49, 377–379 (1973)

    Google Scholar 

  13. Horikawa, E.: On deformations of holomorphic maps. In Proc. Conf. on Manifolds, Tokyo 1973, 383–388

  14. Kodaira, K.: On stability of compact submanifolds of complex manifolds. Amer. J. Math.85, 79–94 (1963)

    Google Scholar 

  15. Kodaira, K.: On the structure of compact complex analytic surfaces. I. Amer. J. Math.86, 751–798 (1964)

    Google Scholar 

  16. Kodaira, K.: Pluricanonical systems on algebraic surfaces of general type. J. Math. Soc. Japan20, 170–192 (1968)

    Google Scholar 

  17. Kodaira, K., Spencer, D. C.: On deformations of complex structures. I. II. Ann. of Math.67, 328–466 (1958)

    Google Scholar 

  18. Kodaira, K., Spencer, D. C.: A theorem of completeness for complex analytic fibre spaces. Acta Math.100, 281–294 (1958)

    Google Scholar 

  19. Kuranishi, M.: On the locally complete families of complex analytic structures. Ann. of Math.75, 536–577 (1962)

    Google Scholar 

  20. Kuranishi, M.: Deformations of compact manifolds. Lecture Notes, Université de Montréal, 1971

  21. Martens, H.: Varieties of special divisors on a curve. II. J. Reine Angew. Math.233, 89–100 (1968)

    Google Scholar 

  22. Mumford, D.: The canonical ring of an algebraic surface. Ann. of Math.76, 612–615 (1962)

    Google Scholar 

  23. Mumford, D.: The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publ. IHES9, 5–22 (1961)

    Google Scholar 

  24. Nakano, S.: On the inverse of monoidal transformation. Publ. RIMS6, 483–502 (1970/71)

    Google Scholar 

  25. Tjurina, G. N.: Resolution of singularities of flat deformations of rational double points. (Russian) Funkcional. Anal. i Priložen4, 77–83 (1970)

    Google Scholar 

  26. Zariski, O.: The theorem of Riemann-Roch for higher multiplies of an effective divisor on an algebraic surface. Ann. of Math.76, 560–612 (1962)

    Google Scholar 

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Horikawa, E. On deformations of quintic surfaces. Invent Math 31, 43–85 (1975). https://doi.org/10.1007/BF01389865

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  • DOI: https://doi.org/10.1007/BF01389865

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