Fano Weighted Complete Intersections of Large Codimension

Abstract

We classify smooth Fano weighted complete intersections of large codimension.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Iskovskikh V. and Prokhorov Yu., Fano Varieties, Springer-Verlag, Berlin (1999) (Encyclopaedia Math. Sci.; 47).

    Google Scholar 

  2. 2.

    Dolgachev I., “Weighted projective varieties,” in: Lect. Notes Math., Springer-Verlag, Berlin, 1982, vol. 956, 34–71.

    Google Scholar 

  3. 3.

    Iano-Fletcher A. R., “Working with weighted complete intersections,” in: Explicit Birational Geometry of 3-Folds, Camb. Univ. Press, Cambridge, 2000, 101–173 (London Math. Soc. Lect. Note Ser.; Vol. 281).

    Google Scholar 

  4. 4.

    Dimca A., “Singularities and coverings of weighted complete intersections,” J. Reine Angew. Math., vol. 366, 183–193 (1986).

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Przyjalkowski V. and Shramov C., “Bounds for smooth Fano weighted complete intersections,” http://arxiv.org/1611.09556.

  6. 6.

    Przyjalkowski V. V. and Shramov C. A., “Automorphisms of weighted complete intersections,” Proc. Steklov Inst. Math., vol. 307, 198–209 (2019).

    MathSciNet  Article  Google Scholar 

  7. 7.

    Pizzato M., Sano T., and Tasin L., “Effective nonvanishing for Fano weighted complete intersections,” Algebra Number Theory, vol. 11, no. 10, 2369–2395 (2017).

    MathSciNet  Article  Google Scholar 

  8. 8.

    Chen J.-J., Chen J., and Chen M., “On quasismooth weighted complete intersections,” J. Algebraic Geom., vol. 20, no. 2, 239–262 (2011).

    MathSciNet  Article  Google Scholar 

  9. 9.

    Przyjalkowski V. and Shramov C., “Hodge level for weighted complete intersections,” Collect. Math. (2020), https://doi.org/10.1007/s13348-019-00276-z.

Download references

Acknowledgments

We are grateful to M. Ovcharenko who found a mistake in the first version of our paper.

Author information

Affiliations

Authors

Corresponding authors

Correspondence to V. V. Przyjalkowski or C. A. Shramov.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 377–384.

V. V. Przyjalkowski was supported by Grant MD-30.2020.1. C. A. Shramov was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS.” Both authors received the award “Young Russian Mathematics” and thank the sponsors and jury.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Przyjalkowski, V.V., Shramov, C.A. Fano Weighted Complete Intersections of Large Codimension. Sib Math J 61, 298–303 (2020). https://doi.org/10.1134/S0037446620020123

Download citation

Keywords

  • weighted complete intersection
  • Fano index
  • codimension