We study the existence and properties of birationally equivalent models for elliptically fibered varieties. In particular these have either the structure of Mori fiber spaces or, assuming some standard conjectures, minimal models with a Zariski decomposition compatible with the elliptic fibration. We prove relations between the birational invariants of the elliptically fibered variety, the base of the fibration and of its Jacobian.

中文翻译：

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高维椭圆纤维化和 Zariski 分解

我们研究了椭圆纤维品种的双有理等价模型的存在和性质。特别是这些具有 Mori 纤维空间的结构，或者假设一些标准猜想，具有与椭圆纤维化兼容的 Zariski 分解的最小模型。我们证明了椭圆纤维变体的双有理不变量、纤维化的基础及其雅可比行列之间的关系。