Preprint
The J -Null Locus and Local Regularity of Weak Solutions of the SemistableJ -Equation
arXiv
arXiv
09/22/2026
DOI: 10.48550/arxiv.2609.26340
Abstract
For the semistableJ -equation, we prove that the numericalJ -null locus coincides with the ambientC² -singular locus of Murakami's weak solution. Consequently, this singular locus is a proper analytic subset with finitely many irreducible components, and the weak solution is locally smooth outside theJ -null locus. The proof relies on two analytic ingredients. First, we establish a regularization theorem for singularJ -subsolutions, showing that Demailly's global regularization preserves quantitative strict cone conditions. Thus, singular strict subsolutions with prescribed analytic poles can be replaced by smooth strict subsolutions away from their pole sets. Second, we derive relative a priori estimates adapted to these subsolutions: a relativeL^(∞) -estimate from determinant control and a weighted second order estimate yielding uniformC² -bounds on compact subsets of the regular locus.
Details
- Title: Subtitle
- The J -Null Locus and Local Regularity of Weak Solutions of the SemistableJ -Equation
- Creators
- Hao FangBiao Ma
- Resource Type
- Preprint
- Publication Details
- arXiv
- DOI
- 10.48550/arxiv.2609.26340
- ISSN
- 2331-8422
- Publisher
- arXiv
- Language
- English
- Date posted
- 09/22/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985236416802771
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