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Title: On a conjecture of Tian
Authors: Ahmadinezhad, Hamid
Cheltsov, Ivan
Schicho, Josef
Keywords: Log canonical threshold
α-invariant of Tian
Smooth surface
Issue Date: 2017
Publisher: © the Authors. Published by Springer Verlag
Citation: AHMADINEZHAD, H., CHELTSOV, I. and SCHICHO, J., 2017. On a conjecture of Tian. Mathematische Zeitschrift, In Press.
Abstract: We study Tian’s α-invariant in comparison with the α1-invariant for pairs (Sd, H) consisting of a smooth surface Sd of degree d in the projective three-dimensional space and a hyperplane section H. A conjecture of Tian asserts that α(Sd, H) = α1(Sd, H). We show that this is indeed true for d = 4 (the result is well known for d 6 3), and we show that α(Sd, H) < α1(Sd, H) for d > 8 provided that Sd is general enough. We also construct examples of Sd, for d = 6 and d = 7, for which Tian’s conjecture fails. We provide a candidate counterexample for S5.
Description: This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/
Version: Published version
DOI: 10.1007/s00209-017-1886-z
URI: https://dspace.lboro.ac.uk/2134/24701
Publisher Link: https://doi.org/10.1007/s00209-017-1886-z
ISSN: 0025-5874
Appears in Collections:Published Articles (Maths)

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