Finite Generation for klt Generalized Pairs
Statement
The BCHM theorem makes the log canonical ring of a projective klt pair finitely generated. Generalized pairs, introduced by Birkar and Zhang, add an auxiliary nef part and have become a central tool in birational geometry, so it is natural to ask whether finite generation survives. It does not: Liu and Wang construct a smooth projective klt generalized pair whose generalized log canonical ring is not a finitely generated algebra.
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construction · #1
GPT-5.6-sol-ultra, Fable 5, Danus, with Jihao Liu and Yanze WangThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
Stated in the abstract, which is unusual: "The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol-ultra, Fable 5, and the Danus system." Remark 1.5 adds that Danus is a specialised agent built on the Rethlas system, and that human verification and polishing were done afterwards.
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