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On a conjecture of Tian
journal contribution
posted on 2017-04-12, 08:40 authored by Hamid Abban, Ivan Cheltsov, Josef SchichoWe 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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Mathematische ZeitschriftCitation
AHMADINEZHAD, H., CHELTSOV, I. and SCHICHO, J., 2017. On a conjecture of Tian. Mathematische Zeitschrift, 288 (1-2), pp.217–241.Publisher
© the Authors. Published by Springer VerlagVersion
- NA (Not Applicable or Unknown)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/Acceptance date
2017-03-20Publication date
2017Notes
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/ISSN
0025-5874eISSN
1432-1823Publisher version
Language
- en