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Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation

  • Jixiang Fu
  • Shing-Tung Yau
  • Dekai Zhang
  • Ziyi Zhang
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Abstract

We study the supercritical LYZ equation on compact Kähler manifolds at the boundary of stability. Under numerical semistability, we prove a quantitative positivity estimate on the modified nef cone. It implies that the destabilizing prime divisors form a finite exceptional family. Assuming the existence of a smooth semisubsolution, we prove that the associated intersection form is negative definite on the span of classes of these divisors. Using this rigidity, we then construct a logarithmic singular subsolution along their union and obtain a bounded Bedford--Taylor solution which is smooth on its complement.

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Cite

BibTeXRIS
BibTeX
@misc{fu2026divisorial,
  title = {{Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation}},
  author = {Jixiang Fu and Shing-Tung Yau and Dekai Zhang and Ziyi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25553},
  eprint = {2609.25553},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25553},
}
RIS
TY  - UNPB
TI  - Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation
AU  - Jixiang Fu
AU  - Shing-Tung Yau
AU  - Dekai Zhang
AU  - Ziyi Zhang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25553
UR  - https://arxiv.org/abs/2609.25553
AB  - We study the supercritical LYZ equation on compact Kähler manifolds at the boundary of stability. Under numerical semistability, we prove a quantitative positivity estimate on the modified nef cone. It implies that the destabilizing prime divisors form a finite exceptional family. Assuming the existence of a smooth semisubsolution, we prove that the associated intersection form is negative definite on the span of classes of these divisors. Using this rigidity, we then construct a logarithmic singular subsolution along their union and obtain a bounded Bedford--Taylor solution which is smooth on its complement.
ER  -