# Books written by Shigefumi Mori.

Shigefumi Mori is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds. He won a Fields Medal in 1990 for the proof of Hartshorne’s conjecture and his work on the classification of three-dimensional algebraic varieties.

## Birational Geometry of Algebraic Varieties

One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond.

## The Resolution of Singular Algebraic Varieties

Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution.

## Moduli Spaces and Arithmetic Geometry

Since its birth algebraic geometry has been closely related to and deeply motivated by number theory. Particularly the modern study of moduli spaces and arithmetic geometry have many important techniques and ideas in common. With this close relation in mind, the RIMS conference Moduli Spaces and Arithmetic Geometry was held at Kyoto University during September 8-15, 2004 as the 13th International Research Institute of the Mathematical Society of Japan. This volume is the outcome of this conference and consists of thirteen papers by invited speakers, including C Soulé, A Beauville and C Faber, and participants.

## Higher Dimensional Birational Geometry

Advanced Studies in Pure Mathematics