Tian’s stabilization problem for toric Fanos

Jin, Chenzi¹ ; Rubinstein, Yanir A¹

¹Department of Mathematics, University of Maryland, College Park, MD, United States

Geometry & topology, Tome 29 (2025) no. 5, pp. 2609-2652

Résumé

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.

Détail

DOI : 10.2140/gt.2025.29.2609

Keywords: alpha invariant, log canonical threshold, Fano variety, toric variety, Tian stabilization problem

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