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arXiv · 2310.02962

On the cone conjecture for log Calabi-Yau mirrors of Fano 3-folds

Jennifer Li
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Abstract

Let $Y$ be a smooth projective $3$-fold admitting a K3 fibration $f : Y \rightarrow \mathbb{P}^1$ with $-K_Y = f^*\mathcal{O}(1)$. We show that the pseudoautomorphism group of $Y$ acts with finitely many orbits on the codimension one faces of the movable cone if $H^3(Y,\mathbb{C})=0$, confirming a special case of the Kawamata--Morrison--Totaro cone conjecture. In [CCGK16], [P18], and [CP18], the authors construct log Calabi-Yau 3-folds with K3 fibrations satisfying the hypotheses of our theorem as the mirrors of Fano 3-folds.

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Jennifer Li. 2023-10-04. On the cone conjecture for log Calabi-Yau mirrors of Fano 3-folds. https://arxiv.org/abs/2310.02962

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