Uniform Székelyhidi conjectures for complex Hessian equations on projective manifolds
Chen, Nie and Xu prove a Nakai–Moishezon-type numerical criterion for a broad class of complex Hessian-type equations on compact projective manifolds. In particular, Corollary 1.3 gives a uniform version of Székelyhidi’s conjecture for complex Hessian quotient equations, while Corollary 1.5 proves the uniform version, formulated by Murakami, for complex k-Hessian equations. However, the results assume projectivity and a uniform numerical condition, whereas Székelyhidi’s original conjecture is formulated for arbitrary compact Kähler manifolds. Thus this should not be recorded as a full solution of the unrestricted original conjecture.
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Occurred: Aug 4, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Editorial metadata: CC BY 4.0; linked content retains its own rights.
Canonical aliases: Uniform Székelyhidi conjectures for complex Hessian equations on projective manifolds · Uniform Székelyhidi conjectures
Confidence: Not scored
Registry verification: unreviewed · preprint · partial
Attribution
VibeMathed
registry · event recorded by
Gao Chen
human · human collaborator
Sijie Nie
human · human collaborator
Yulun Xu
human · human collaborator
ChatGPT 5.6 Sol
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Yulun Xu
This event attributed to Sijie Nie
This event attributed to Gao Chen
This event attributed to ChatGPT 5.6 Sol
Chen, Nie and Xu prove a Nakai–Moishezon-type numerical criterion for a broad class of complex Hessian-type equations on compact projective manifolds. In particular, Corollary 1.3 gives a uniform version of Székelyhidi’s conjecture for complex Hessian quotient equations, while Corollary 1.5 proves the uniform version, formulated by Murakami, for complex k-Hessian equations. However, the results assume projectivity and a uniform numerical condition, whereas Székelyhidi’s original conjecture is formulated for arbitrary compact Kähler manifolds. Thus this should not be recorded as a full solution of the unrestricted original conjecture. parent of this event
Uniform Székelyhidi conjectures for complex Hessian equations on projective manifolds evidence for this event
Uniform Székelyhidi conjectures for complex Hessian equations on projective manifolds parent of this event
VibeMathed record: Uniform Székelyhidi conjectures for complex Hessian equations on projective manifolds evidence for this event
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