Shigefumi Mori is an esteemed mathematician known for his significant contributions to the field of algebraic geometry. His groundbreaking work in algebraic geometry focuses on the classification of algebraic varieties, a fundamental problem in the field. Mori’s achievements have earned him international recognition, including the prestigious Fields Medal in 1990.

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Mori completed his education at Kyoto University and received his B.A. and M.A. degrees in 1973 and 1975, respectively. He made major progress in classifying algebraic surfaces, following the footsteps of great Italian algebraic geometers. In 1978, Mori proved the Hartshorne conjecture, which claimed that projective spaces are the only smooth complete algebraic varieties with ample tangent bundles.

Throughout his career, Mori has made significant contributions to the classification of Fano 3-folds and has worked on the minimal model program, revolutionizing the understanding of higher dimensional algebraic varieties. In addition to his numerous awards and honors, Mori has authored several important publications, including “Birational geometry of algebraic varieties” coauthored with János Kollár.

### Key Takeaways:

- Shigefumi Mori is a renowned mathematician known for his groundbreaking work in algebraic geometry.
- His contributions focus on the classification of algebraic varieties, a fundamental problem in the field.
- Mori’s achievements include proving the Hartshorne conjecture, classifying Fano 3-folds, and revolutionizing the understanding of higher dimensional algebraic varieties.
- He was awarded the prestigious Fields Medal in 1990 for his significant contributions to mathematics.
- Mori has authored important publications, including “Birational geometry of algebraic varieties” coauthored with János Kollár.

## Shigefumi Mori’s Career and Awards

Shigefumi Mori’s career in mathematics has been marked by numerous achievements and accolades. After completing his Ph.D., Mori held positions at Kyoto University and the University of Nagoya, where he was promoted to full professor in 1988. He has also spent significant time in the United States as a visiting professor at prestigious institutions such as Harvard, the Institute for Advanced Study, Columbia University, and the University of Utah.

Mori’s contributions to the field have been widely recognized. Before receiving the Fields Medal in 1990, he had already received awards and prizes such as the Yanaga Prize and the Chunichi Culture Prize in Japan. In addition to the Fields Medal, Mori has been honored with the AMS Cole Prize in Algebra and the Cole Prize for algebra from the American Mathematical Society. He is a member of the Japan Academy and has been recognized as a foreign honorary member of the American Academy of Arts and Sciences and a foreign associate of the US National Academy of Sciences.

Throughout his career, Mori has published numerous papers on varied topics, including rational curves on algebraic varieties, canonical bundle formulas, and the classification of singular surfaces of general type.

### Shigefumi Mori’s Awards and Honors

Award/Honor | Year |
---|---|

Fields Medal | 1990 |

AMS Cole Prize in Algebra | 1991 |

Cole Prize for Algebra | 1994 |

Yanaga Prize | 1987 |

Chunichi Culture Prize | 1989 |

Table: Shigefumi Mori’s Awards and Honors

Shigefumi Mori’s dedication to his research and his exceptional mathematical achievements have earned him numerous awards and honors throughout his illustrious career. His contributions to the field of algebraic geometry, particularly his work on the classification of algebraic varieties, have revolutionized the understanding of higher dimensional spaces.

Stay tuned for the next section, where we will explore the significance of Mori’s program in birational geometry.

## The Significance of Mori’s Program in Birational Geometry

Shigefumi Mori, a renowned mathematician, has made significant breakthroughs in the field of mathematics through his groundbreaking research. One of his most significant contributions is the development of what is now known as “Mori’s program” or the minimal model program. This program has revolutionized the study of birational geometry, providing a framework to understand and classify algebraic varieties.

Mori’s program introduced a new perspective in the field, shifting the focus from linear systems to extremal rays and faces of cones. By understanding the behavior of these extremal rays, mathematicians gained valuable insights into the classification of various types of contractions, such as divisorial contractions and flips. This approach has opened up new avenues of research, particularly in higher dimensions, and has greatly expanded our understanding of birational geometry.

Although Mori never published a formal document outlining his program, his initial work and subsequent contributions from other mathematicians have deepened our understanding of the minimal model program. His research on extremal curve neighborhoods and the classification of terminal 3-fold singularities has played a crucial role in advancing the field.

Mori’s program has had a profound impact on the study of birational geometry, allowing mathematicians to unravel the complexities of algebraic varieties in a systematic way. His mathematical breakthroughs continue to shape the field, inspiring further research and advancements in the understanding of geometry and its applications.

## FAQ

### What are Shigefumi Mori’s major contributions to algebraic geometry?

Shigefumi Mori is known for his groundbreaking work in algebraic geometry, particularly in the classification of algebraic varieties. He made significant progress in classifying algebraic surfaces and proved the Hartshorne conjecture in 1978, earning him the prestigious Fields Medal in 1990. He has also made contributions to the classification of Fano 3-folds and the development of the minimal model program.

### Where did Shigefumi Mori complete his education?

Shigefumi Mori completed his education at Kyoto University, where he received his B.A. and M.A. degrees in 1973 and 1975, respectively.

### What is the minimal model program that Shigefumi Mori developed?

The minimal model program, also known as Mori’s program, is a mathematical framework developed by Shigefumi Mori. It revolutionized the field of birational geometry and provided a method to understand and classify algebraic varieties. The program allowed for the classification of various types of contractions and led to advancements in the understanding of morphisms of varieties.

### What awards and honors has Shigefumi Mori received?

Shigefumi Mori has received numerous awards and honors throughout his career. In addition to the Fields Medal in 1990, he has been honored with the AMS Cole Prize in Algebra and the Cole Prize for algebra from the American Mathematical Society. He is a member of the Japan Academy and has been recognized as a foreign honorary member of the American Academy of Arts and Sciences and a foreign associate of the US National Academy of Sciences.

### What are some of Shigefumi Mori’s publications?

Shigefumi Mori has authored several important publications in the field of algebraic geometry. One notable publication is “Birational geometry of algebraic varieties,” which he coauthored with János Kollár. He has also published papers on topics such as rational curves on algebraic varieties, canonical bundle formulas, and the classification of singular surfaces of general type.

### How has Mori’s program impacted the field of birational geometry?

Mori’s program, or the minimal model program, has had a profound impact on the study of birational geometry. It provided a framework to understand and classify algebraic varieties and revolutionized the approach to morphisms of varieties. The program shifted the focus from linear systems to extremal rays and faces of cones, opening up new avenues of research in higher dimensions. Mori’s work on extremal curve neighborhoods and the classification of terminal 3-fold singularities has paved the way for advancements in the field.