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Projective models of enriques surfaces

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References

  1. Artin, M.: On enriques surfaces. Doctoral Thesis, Harvard University 1960

  2. Artin, M.: Some numerical criteria for contractability of curves on algebraic surfaces. Am J. Math.84, 485–496 (1962); On isolated singularities of surfaces. Am. J. Math.88, 129–136 (1966)

    Google Scholar 

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

    Google Scholar 

  4. Beauville, A.: Surfaces algebriques complexes. Astérisque54, 1978

  5. Coble, A.: Algebraic geometry and theta functions. Vol. X Publ. Am. Math. Soc. 1981

  6. Cossec, F.R.: On Reye congruences. Trans. Am. Math. Soc. (to appear)

  7. Demazure, M. et al.: Séminaire son les singularités des surfaces. Springer Lectures Notes in Mathematics, Vol. 777. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  8. Fano, G.: Nuovo rierche sulle congruenze di retta del 3° ordine. Mem. Accad. Sci. Cl. Sci. Fis. Mat. Natur. Torino50, 1–79 (1901); Superficie algebriche di genere zero e bigenere uno e loro casi particolari. Rend. Circ. Mat. Palermo29, 98–118 (1910)

    Google Scholar 

  9. Hartshorne, R.: Algebraic geometry. Graduate Texts in mathematics, Vol. 52. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  10. Horikawa, E.: On the periods of Enriques surfaces. I. Math. Ann.234, 73–88 (1978)

    Google Scholar 

  11. Horikawa, E.: On deformations of quintic surfaces. Invent. Math.31, 43–85 (1975)

    Google Scholar 

  12. Kodaira, K.: On compact analytic surfaces. II. Ann. Math.77, 563–626 (1963)

    Google Scholar 

  13. Lang, W.E.: Quasi-elliptic surfaces in characteristic three. Ann. Sci. Ecole Norm. sup.12, 473–500 (1979)

    Google Scholar 

  14. Mumford, D.: Enriques classification of surfaces in charp. Part I. In: Global analysis. Princeton: Princeton University Press 1969; Part II. In: Complex analysis and algebraic geometry. Cambridge: Cambridge University Press 1977

    Google Scholar 

  15. Nagata, M.: On rational surfaces. I. Mem. Coll. Sci. Univ. Kyoto Ser. A Math.32, 351–370 (1969)

    Google Scholar 

  16. Reye, T.: Geometrie der lage (2nd Edn.) Leipzig 1882

  17. Safarevic, I.R. et al.: Algebraic surfaces. Proc. Steklov Inst. Math.75 (1965) [Engl. Transl. Am. Math. Soc. (1967)]

  18. Saint-Donat, B.: Projective models of K3 surfaces. Am. J. Math.96, 602–639

  19. Serre, J.P.: Cours d'arithmétique. Paris: Presses Universitaires de France 1970

    Google Scholar 

  20. Segre, C.: Surfaces du 4e ordre à conique double. Math. Ann.24, 313–344 (1884)

    Google Scholar 

  21. Shah, J.: Projective degenerations of Enriques surfaces. Math. Ann.256, 475 (1981)

    Google Scholar 

  22. Wall, C.T.C.: On classification of cubic surfaces. J. London Math. Soc.19, 245–256 (1979)

    Google Scholar 

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The author would like to mention that this study is an elaborated version of a part of his Yale Ph.D. thesis, and take this opportunity to express his gratitude to his thesis advisor Bernard Saint-Donat as well as to M. Schlessinger, J. Wahl, and M. Nori for stimulating discussions. We would also like to thank P. Russell for allowing us to write the final version of this paper at the University of McGill

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Cossec, F.R. Projective models of enriques surfaces. Math. Ann. 265, 283–334 (1983). https://doi.org/10.1007/BF01456021

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