The K-global F-regularity conjecture for semiample anticanonical pairs

Let (X,B)(X,B) be a normal projective complex pair with klt singularities such that KXB-K_X-B is semiample. K-global F-regularity conjecture. For every model (X,B)Spec(A)(\mathcal{X},\mathcal{B})\to\operatorname{Spec}(A) of (X,B)(X,B), the locus

{pSpec(A) | (Xp,Bp) is K-globally F-regular}\left\{\mathfrak{p}\in\operatorname{Spec}(A)\ \middle|\ (X_{\mathfrak{p}},B_{\mathfrak{p}})\text{ is K-globally F-regular}\right\}

is dense in Spec(A)\operatorname{Spec}(A). This extends the expected dense reduction behavior from log Calabi--Yau and log Fano settings to semiample anticanonical klt pairs; the source does not state a resolution.

Sources & referencesView supporting material

Primary source

Marta Benozzo, Iacopo Brivio and Chi-Kang Chang, “On the superadditivity of anticanonical Iitaka dimension”, arXiv:2309.16580 (2026).

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