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arXiv · 2504.04109

Variation of cones of divisors in a family of varieties -- Fano type case

Sung Rak Choi·Zhan Li·Chuyu Zhou
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Abstract

We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of N\'eron-Severi spaces, nef cones, effective cones, movable cones, and Mori chamber decompositions for a family of Fano type varieties after a generically finite base change. Additionally, we show the uniform behavior of the minimal model program for this family. These results are applied to the boundedness problem of Fano type varieties.

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Sung Rak Choi, Zhan Li, Chuyu Zhou. 2025-04-05. Variation of cones of divisors in a family of varieties -- Fano type case. https://arxiv.org/abs/2504.04109

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