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Abstract

We study a number of conditions equivalent to homology to0 of vanishing cycles on a non-singular complex projective surface, and we classify such surfaces.

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  1. M. Kh. Gizatullin, “On affine surfaces that can be completed by a nonsingular rational curve,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, No. 4, 778–802 (1970).

    Google Scholar 

  2. P. Deligne, A. Grothendieck, and N. Katz, “Théorémes de monodromie,” SGA VII (2) (1973); to appear in: Lecture Notes in Mathematics.

  3. I. V. Dolgachev, “On the purity of degeneration loci of families of curves,” Invent. Math.,8, No. 1, 34–54 (1969).

    Google Scholar 

  4. A. B. Zhizhenko, “Homology groups of algebraic varieties,” Izv. Akad. Nauk SSSR, Ser. Matem.,25, No. 6, 765–788 (1961).

    Google Scholar 

  5. J. Milnor, Singular Points of Complex Hypersurfaces, Princeton University Press, Princeton (1968).

    Google Scholar 

  6. B. G. Moishezon, “Algebraic homology classes on algebraic varieties,” Izv. Akad. Nauk SSSR, Ser. Matem.,31, No. 2, 225–268 (1967).

    Google Scholar 

  7. G. N. Tyurina, “The topological properties of isolated singularities of complex spaces of codimension 1,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 3, 605–620 (1968).

    Google Scholar 

  8. I. R. Shafarevich, Lectures on Minimal Models and Birational Transformations of Two-Dimensional Schemes, Bombay (1966).

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Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 869–880, June, 1973.

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Zak, F.L. Surfaces with zero Lefschetz cycles. Mathematical Notes of the Academy of Sciences of the USSR 13, 520–525 (1973). https://doi.org/10.1007/BF01163961

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  • DOI: https://doi.org/10.1007/BF01163961

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