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Some conic bundless

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Abstract

A representation of the anticanonical K3 surface of a singular pencil of conics is described. This generalizes the well-known Shokurov theorem.

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References

  1. S. Mori, “Flip theorem and the existence of minimal models for 3-folds,”J. Amer. Math. Soc.,1, 117–253 (1988).

    MATH  MathSciNet  Google Scholar 

  2. V. A. Iskovskikh,Lectures on Three-Dimensional Algebraic Varieties: Fano Varieties [in Russian], Izd. Moskov. Univ., Moscow (1988).

    Google Scholar 

  3. V. V. Shokurov, “Smoothness of a general anticanonical divisor on a Fano variety,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],43, 430–441 (1979).

    MATH  MathSciNet  Google Scholar 

  4. M. Reid,Projective Morphism According to Kawamata, Preprint, Warwick (1983).

  5. Yu. G. Prokhorov, “On three-dimensional varieties with hyperplane sections-Enriques surfaces,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],186, No. 9, 113–124 (1995).

    MATH  MathSciNet  Google Scholar 

  6. H. Clemens, J. Kollar, and S. Mori,Higher Dimensional Complex Geometry, A Summer Seminar at the Univ. of Utah, Salt Lake City, 1987, Soc. Math. de France (1988).

  7. Y. Kawamata, K. Matsuda, and K. Matsuki, “Introduction to the minimal model problem,” in:Algebraic Geometry. Proc. Symp., Sendai, 1985, Vol. 10, Adv., Stud. Pure Math, Kinokuniya, Tokyo (1987), pp. 283–360.

    Google Scholar 

  8. V. Alexeev, “General elephants of ℚ-Fano 3-folds,”Compositio Math.,91, No. 1, 91–116 (1994).

    MATH  MathSciNet  Google Scholar 

  9. V. A. Alexeev, “Theorems about good divisors on log Fano varieties (case of indexr>n−2),” in:Algebraic Geometry. Proc. US-USSR Symp., 1989, Vol. 1479, Lecture Notes in Math, Springer, Chicago (I.L.) (1991), pp. 1–9.

    Google Scholar 

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    I. Yu. Fedorov

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  1. I. Yu. Fedorov
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Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 903–910, June, 1998.

The author is greatly indebted to V. A. Iskovskikh, Yu. G. Prokhorov, and I. A. Chel'tsov for fruitful discussions.

This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00820 and by INTAS under grant No. 93-2805.00-00-00.

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Fedorov, I.Y. Some conic bundless. Math Notes 63, 796–801 (1998). https://doi.org/10.1007/BF02312774

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