Geodesic
Nef cones of fiber products and an application to the cone conjecture
Forum of Mathematics, Sigma, Tome 12 (2024)

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We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron–Severi space decomposes. We apply it to describe the nef cone of so-called Schoen varieties, which are the higher-dimensional analogues of the Calabi–Yau threefolds constructed by Schoen. Schoen varieties give rise to Calabi–Yau pairs, and in each dimension at least three, there exist Schoen varieties with nonpolyhedral nef cone. We prove the Kawamata–Morrison–Totaro cone conjecture for the nef cones of Schoen varieties, which generalizes the work by Grassi and Morrison. 
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     author = {C\'ecile Gachet and Hsueh-Yung Lin and Long Wang},
     title = {Nef cones of fiber products and an application to the cone conjecture},
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Cécile Gachet; Hsueh-Yung Lin; Long Wang. Nef cones of fiber products and an application to the cone conjecture. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.22

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