The K-semistable degeneration conjecture for Fano threefolds of Family 2.16

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Let XX be a K-semistable Q\mathbb{Q}-Gorenstein degeneration of a smooth Fano threefold of Family \textnumero 2.16. Degeneration conjecture. XX is isomorphic to the blow-up of a (2,2)(2,2)-complete intersection in P5\mathbb{P}^5 along a conic curve. The claim is identified in the source as the most technical step of the proposed description of the K-moduli space; the excerpt does not state whether it has been proved or remains open.

References

Primary source

Ivan Cheltsov, DongSeon Hwang, Alex Küronya, Antonio Laface, Frédéric Mangolte, Alex Massarenti, Jihun Park and Junyan Zhao, “On K-stability of Fano's last Fanos”, arXiv:2507.08528 (2026).

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