Uniform Székelyhidi conjectures for complex Hessian equations on projective manifolds
Statement
We prove a Nakai-Moishezon-type criterion for complex Hessian-type equations on projective manifolds whose associated degree-n polynomials are strongly strictly right-Noetherian. For strictly right-Noetherian polynomials of arbitrary degree, we prove a uniform Nakai-Moishezon-type criterion. This class includes the complex Hessian and Hessian quotient equations.
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proof attempt · #1
Gao Chen, Sijie Nie and Yulun Xu, using ChatGPT 5.6 SolThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The authors state that the proofs of the cone-inclusion lemmas in Section 3 are revised versions of arguments generated by ChatGPT 5.6 Sol. The authors subsequently checked and edited those arguments for mathematical clarity. ChatGPT 5.6 Sol also identified gaps in an earlier version of the manuscript and assisted with grammar correction. The Section 3 cone-inclusion lemmas are then used in Section 4 to prove the uniform Székelyhidi-type results.
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