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Tian's stabilization
problem for toric Fanos
Chenzi Jin and Yanir A Rubinstein |
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Geometry & Topology 29 (2025) 2609–2652
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Abstract |
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In 1988, Tian posed the stabilization problem for equivariant global log canonical thresholds. We solve it in the case of toric Fano manifolds. This is the first general result on Tian’s problem. A key new estimate involves expressing complex singularity exponents associated to orbits of a group action in terms of support and gauge functions from convex geometry. These techniques also yield a resolution of another conjecture of Tian from 2012 on more general thresholds associated to Grassmannians of plurianticanonical series. |
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In memory of Eugenio Calabi |
Keywords
alpha invariant, log canonical threshold, Fano variety,
toric variety, Tian stabilization problem
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Mathematical Subject Classification
Primary: 14C20, 14J45, 14J50, 14M25
Secondary: 14L30, 32Q20, 32U05, 52A40
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References |
Publication
Received: 30 March 2024
Revised: 10 October 2024
Accepted: 14 December 2024
Published: 14 August 2025
Proposed: Gang Tian
Seconded: Arend Bayer, Tobias H Colding
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Authors |
| Chenzi Jin | |
| Department of Mathematics University of Maryland College Park, MD United States |
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| Yanir A Rubinstein | |
| Department of Mathematics University of Maryland College Park, MD United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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