Birational geometry of algebraic varieties

TL;DR

This paper reviews recent advances in birational geometry, emphasizing the minimal model program, Fano varieties, and singularities in characteristic zero, highlighting key developments and current research directions.

Contribution

It provides a comprehensive overview of recent progress in birational geometry, summarizing major results and open problems in the field.

Findings

Progress in the minimal model program

Classification results for Fano varieties

Advances in understanding singularities

Abstract

This is a report on some of the main developments in birational geometry in the last few years focusing on the minimal model program, Fano varieties, singularities and related topics, in characteristic zero.