# Higher Dimensional Elliptic Fibrations and Zariski Decompositions

## TL;DR

This paper investigates the birational models of elliptically fibered varieties, focusing on their existence, properties, and relations between invariants, especially concerning Zariski decompositions and minimal models.

## Contribution

It introduces new results on the existence of minimal models with compatible Zariski decompositions for elliptic fibrations, under certain conjectures.

## Key findings

- Existence of birational models as Mori fiber spaces or minimal models
- Relations between birational invariants of the total space, base, and Jacobian
- Conditions under which Zariski decompositions are compatible with elliptic fibrations

## Abstract

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.