K-stability of Log Fano Cone Singularities
Name
Huang-kaihuang-phd-math-2022-thesis.pdf
Description
Thesis PDF
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548.55 KB
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Adobe PDF
Checksum (MD5)
0103c2cee46050f1e57d61f3841f5a71
Author(s)
Huang, Kai
Advisor(s)
Xu, Chenyang
Date Issued
May 2022
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we define the 𝛿-invariant for log Fano cone singularities, and show that the necessary and sufficient condition for K-semistability is 𝛿 ≥ 1. This generalizes the result of C. Li and K. Fujita. We also prove that on any log Fano cone singularity of dimension 𝑛 whose 𝛿-invariant is less than (𝑛+1)/𝑛, any valuation computing 𝛿 has a finitely generated associated graded ring. This shows a log Fano cone is K-polystable if and only if it is uniformly K-stable. Together with earlier works, this implies the Yau-Tian-Donaldson Conjecture for Fano cone.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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