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arXiv · 2210.02779

Nef cones of fiber products and an application to the Cone Conjecture

Cécile Gachet·Hsueh-Yung Lin·Long Wang
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Abstract

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 non-polyhedral 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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Cécile Gachet, Hsueh-Yung Lin, Long Wang. 2024-03-01. Nef cones of fiber products and an application to the Cone Conjecture. https://arxiv.org/abs/2210.02779

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