We characterize a k-th accumulation point of pseudo-effective thresholds of n-dimensional varieties as certain invariant associates to a numerically trivial pair of an \((n-k)\)-dimensional variety. This characterization is applied towards Fujita’s log spectrum conjecture for large k.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Birkar, C., Cascini, P., Hacon, C.D., McKernan, J.: Existence of minimal models for varieties of log general type. J. Am. Math. Soc. 23(2), 405–468 (2010)
Birkar, C.: Singularities of linear systems and boundedness of Fano varieties (2016). arXiv:1609.05543
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)
Di Cerbo, G.: On Fujita’s log spectrum conjecture. Math. Ann. 366(1–2), 447–457 (2016)
Di Cerbo, G.: On Fujita’s spectrum conjecture. Adv. Math. 311, 238–248 (2017)
Fujita, T.: On Kodaira energy and adjoint reduction of polarized manifolds. Manuscr. Math. 76(1), 59–84 (1992)
Fujita, T.: On Kodaira energy of polarized log varieties. J. Math. Soc. Jpn. 48(1), 1–12 (1996)
Han, J., Li, Z.: On Fujita’s conjecture for pseudo-effective thresholds. Math. Res. Lett. (2017). arXiv:1705.08862
Han, J., Li, Z.: Weak Zariski decompositions and log terminal models for generalized polarized pairs (2018). arXiv:1806.01234
Hacon, C.D., McKernan, J., Chenyang, X.: ACC for log canonical thresholds. Ann. Math. (2) 180(2), 523–571 (2014)
Kollár, J., et al.: Flips and Abundance for Algebraic Threefolds. Société Mathématique de France, Paris (1992)
Li, Z.: Fujita’s conjecture on iterated accumulation points of pseudo-effective thresholds (2018). arXiv:1812.04262
McKernan, J., Prokhorov, Y.: Threefold thresholds. Manuscr. Math. 114(3), 281–304 (2004)
Shokurov, V.V.: Problems about Fano varieties. In: Birational Geometry of Algebraic Varieties, Open Problems. The XXIIIrd International Symposium, Division of Mathematics, The Taniguchi Foundation, pp. 30–32 (1988)
Shokurov, V.V.: Three-dimensional log perestroikas. Izv. Ross. Akad. Nauk Ser. Mat. 56(1), 105–203 (1992)
J. H. thanks his advisor Gang Tian for constant supports and encouragement. Z. L. thanks Chen Jiang for extensive discussions on special cases related to the problem. The first part of the paper was completed in the summer of 2017 while Z. L. stayed at the University of Lübeck and he thanks the quiet environment provided by the Zentrale Hochschulbibliothek Lübeck. Both authors thank Chenyang Xu for constant supports. Both authors also thank the anonymous referee for carefully reading the manuscript and providing constructive suggestions. This work is partially supported by NSFC Grant No. 11601015.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Han, J., Li, Z. On accumulation points of pseudo-effective thresholds. manuscripta math. (2020). https://doi.org/10.1007/s00229-020-01220-3
Mathematics Subject Classification