Skip to main content
Log in

Birational geometry of singular Fano varieties

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

We prove the divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. V. Pukhlikov, “Birational Geometry of Fano Direct Products,” Izv. Ross. Akad. Nauk, Ser. Mat. 69(6), 153–186 (2005) [Izv. Math. 69, 1225–1255 (2005)].

    MathSciNet  Google Scholar 

  2. A. V. Pukhlikov, “Birationally Rigid Varieties. I: Fano Varieties,” Usp. Mat. Nauk 62(5), 15–106 (2007) [Russ. Math. Surv. 62, 857–942 (2007)].

    MathSciNet  Google Scholar 

  3. A. V. Pukhlikov, “Birationally Rigid Fano Hypersurfaces with Isolated Singularities,” Mat. Sb. 193(3), 135–160 (2002) [Sb. Math. 193, 445–471 (2002)].

    MathSciNet  Google Scholar 

  4. A. V. Pukhlikov, “Birational Automorphisms of Fano Hypersurfaces,” Invent. Math. 134(2), 401–426 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  5. I. Cheltsov, “Fano Varieties with Many Selfmaps,” Adv. Math. 217(1), 97–124 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  6. Flips and Abundance for Algebraic Threefolds, Ed. by J. Kollár (Soc. Math. France, Paris, 1992), Astérisque 211.

    MATH  Google Scholar 

  7. I. A. Cheltsov, “Log Canonical Thresholds on Hypersurfaces,” Mat. Sb. 192(8), 155–172 (2001) [Sb. Math. 192, 1241–1257 (2001)].

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Pukhlikov.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 165–183.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pukhlikov, A.V. Birational geometry of singular Fano varieties. Proc. Steklov Inst. Math. 264, 159–177 (2009). https://doi.org/10.1134/S0081543809010180

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543809010180

Keywords

Navigation