The common relative Jacobian conjecture for Type i KSS pairs

Let (Ai,Bi)(A_i,B_i), for i=1,,12i=1,\ldots,12, be one of the twelve Type ii KSS pairs of smooth elliptic Calabi--Yau 33-folds over P2\mathbb{P}^2, with elliptic fibrations fi ⁣:AiP2f_i\colon A_i\to\mathbb{P}^2 and gi ⁣:BiP2g_i\colon B_i\to\mathbb{P}^2. A relative Jacobian is the relative elliptic fibration associated to an elliptic fibration. Common relative Jacobian conjecture. The elliptic fibrations fif_i and gig_i share the same relative Jacobian πi ⁣:JiP2\pi_i\colon J_i\to\mathbb{P}^2. The paper's abstract states that this claim is proved for every pair, so it is no longer open.

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Primary source

Hayato Morimura, “Totaro–Vial lemma in F-theory”, arXiv:2301.12751 (2024).

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