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

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.

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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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