Abstract
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 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.
Publisher
Cambridge University Press (CUP)
Reference50 articles.
1. [20] Ito, A. , Lai, C.-J. and Wang, S.-S. , ‘The movable cone of Calabi–Yau threefolds in ruled Fano manifolds’, J. Geom. Phys. 195 (2024), Paper No. 105053, 21.
2. Hilbert’s 14th problem over finite fields and a conjecture on the cone of curves;Totaro;Compos. Math.,2008
3. [10] Dinh, T.-C. , Gachet, C. , Lin, H.-Y. , Oguiso, K. , Wang, L. , and Yu, X. , ‘Smooth projective surfaces with infinitely many real forms’, Preprint, 2023, arXiv: 2210.04760v2.
4. Algebraic Geometry
5. The cone conjecture for Calabi–Yau pairs in dimension 2;Totaro;Duke Math. J.,2010