Fujita’s conjecture on iterated accumulation points of pseudo-effective thresholds

Abstract

We show that k-th iterated accumulation points of pseudo-effective thresholds of n-dimensional varieties are bounded by \(n-k+1\).

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Beltrametti, M.C., Sommese, A.J.: The Adjunction Theory of Complex Projective Varieties De. Gruyter Expositions in Mathematics, vol. 16. Walter de Gruyter & Co., Berlin (1995)

    Google Scholar 

  2. 2.

    Birkar, C., Zhang, D.-Q.: Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Publ. Math. Inst. Hautes Études Sci. 123, 283–331 (2016)

    MathSciNet  Article  Google Scholar 

  3. 3.

    Di Cerbo, G.: On Fujita’s log spectrum conjecture. Math. Ann. 366(1–2), 447–457 (2016)

    MathSciNet  Article  Google Scholar 

  4. 4.

    Di Cerbo, G.: On Fujita’s spectrum conjecture. Adv. Math. 311, 238–248 (2017)

    MathSciNet  Article  Google Scholar 

  5. 5.

    Fujita, T.: Classification theories of polarized varieties London. Mathematical Society Lecture Note Series, vol. 155. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  6. 6.

    Fujita, T.: On Kodaira energy and adjoint reduction of polarized manifolds. Manuscripta Math. 76(1), 59–84 (1992)

    MathSciNet  Article  Google Scholar 

  7. 7.

    Fujita, T.: On Kodaira energy of polarized log varieties. J. Math. Soc. Japan 48(1), 1–12 (1996)

    MathSciNet  Article  Google Scholar 

  8. 8.

    Fujino, O.: On subadditivity of the logarithmic Kodaira dimension. J. Math. Soc. Japan 69(4), 1565–1581 (2017)

    MathSciNet  Article  Google Scholar 

  9. 9.

    Fujino, O.: Corrigendum: On subadditivity of the logarithmic Kodaira dimension. J. Math. Soc. Japan 72(4), 1181–1187 (2020)

    MathSciNet  Article  Google Scholar 

  10. 10.

    Han, J., and Li, Z.: On accumulation points of pseudo-effective thresholds. To appear at Manuscripta Math., (2020)

  11. 11.

    Han, J., Li, Z.: On Fujita’s conjecture for pseudo-effective thresholds. Math. Res. Lett. 27(2), 377–396 (2020)

    MathSciNet  Article  Google Scholar 

  12. 12.

    Hacon, C. D., McKernan, J., and Xu, C.: ACC for log canonical thresholds. Ann. of Math. 2, 180(2):523–571,(2014)

  13. 13.

    Höring, A.: The sectional genus of quasi-polarised varieties. Arch. Math. (Basel) 95(2), 125–133 (2010)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Lesieutre, J.: Notions of numerical Iitaka dimension do not coincide. arXiv:1904.10832, (2019)

  15. 15.

    Nakayama, N.: Zariski-decomposition and abundance. MSJ Memoirs, vol. 14. Mathematical Society of Japan, Tokyo (2004)

    Google Scholar 

  16. 16.

    Shokurov, V.V.: A nonvanishing theorem. Izv. Akad. Nauk SSSR Ser. Mat. 49(3), 635–651 (1985)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This paper is a continuation of the previous joint work with Jingjun Han [10]. The author thanks Chen Jiang for simplifying the original argument of Proposition 3.2. This work is partially supported by NSFC Grant No.11601015 and a starting grant from SUSTech.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Zhan Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, Z. Fujita’s conjecture on iterated accumulation points of pseudo-effective thresholds. Sel. Math. New Ser. 27, 9 (2021). https://doi.org/10.1007/s00029-021-00622-9

Download citation

Mathematics Subject Classification

  • 14E30