Birational Geometry of 3-fold Mori Fibre Spaces

TL;DR

This paper explores the birational geometry and classification of 3-fold Mori fiber spaces, specifically conic bundles over P^2 and cubic del Pezzo fibrations over P^1, providing explicit examples and raising open questions.

Contribution

It offers a detailed analysis of the birational properties of 3-fold Mori fiber spaces, including explicit examples and new insights into their geography.

Findings

Classification of 3-fold conic bundles over P^2

Analysis of cubic del Pezzo fibrations over P^1

Identification of open questions in the birational geometry of these spaces

Abstract

We study the geography and birational geometry of 3-fold conic bundles over P^2 and cubic del Pezzo fibrations over P^1. We discuss many explicit examples and raise several open questions. This paper was submitted to the proceedings of the "Fano conference" held in Torino in October 2002.