Birational geometry of threefolds

Abstract

In this article, we survey various recent results on explicit birational geometry in dimension three. We explain the notion of packings of baskets introduced by Meng Chen and the author. We also demonstrate applications including pluricanonical maps of threefolds of general type, Fano threefolds and weighted complete intersections. Second part of the article is devoted to survey the joint work of Christopher Hacon and the author on factoring birational maps in dimension three.