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

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Abstract

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

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References

  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)

    Book  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

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

    Article  MathSciNet  Google Scholar 

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

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

    Article  MathSciNet  Google Scholar 

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

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

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

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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.

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  1. Department of Mathematics, Southern University of Science and Technology, 1088 Xueyuan Rd, Shenzhen, 518055, China

    Zhan Li

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  1. Zhan Li
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Correspondence to Zhan Li.

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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

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