mathematics

Shigefumi Mori

Shigefumi Mori is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Shigefumi Mori rather than just read about it. In short: Shigefumi Mori (森重文, Mori Shigefumi; born February 23, 1951) is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds. He won the Fields Medal in 1990.

Key takeaways

Shigefumi Mori belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Shigefumi Mori to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Shigefumi Mori from memory before moving on to harder problems.

Reference excerpt

Shigefumi Mori (森重文, Mori Shigefumi; born February 23, 1951) is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds. He won the Fields Medal in 1990.

Career Mori completed his Ph.D. titled "The Endomorphism Rings of Some Abelian Varieties" under Masayoshi Nagata at Kyoto University in 1978. He was a visiting professor at Harvard University during 1977–1980, the Institute for Advanced Study in 1981–82, Columbia University 1985–87 and the University of Utah for periods during 1987–89 and again during 1991–92. He has been a professor at Kyoto University since 1990.

Work

He generalized the classical approach to the classification of algebraic surfaces to the classification of algebraic three-folds. The classical approach used the concept of minimal models of algebraic surfaces. He found that the concept of minimal models can be applied to three-folds as well if we allow some singularities on them. The extension of Mori's results to dimensions higher than three is called the minimal model program and is an active area of research in algebraic geometry. He has been elected president of the International Mathematical Union, becoming the first head of the group from East Asia.

Awards He was awarded the Fields Medal in 1990 at the International Congress of Mathematicians. In 2021, he received the Order of Culture.

Major publications

Mori, Shigefumi (1979). "Projective Manifolds with Ample Tangent Bundles". Annals of Mathematics. 110 (3): 593–606. doi:10.2307/1971241. JSTOR 1971241. Mori, Shigefumi; Mukai, Shigeru (1981). "Classification of Fano 3-folds with B2 ≥ 2". Manuscripta Mathematica. 36 (2): 147–162. doi:10.1007/BF01170131. S2CID 189831516. Mori, Shigefumi; Mukai, Shigeru (2003). "Classification of Fano 3-folds with B2 ≥ 2. (Erratum)". Manuscripta Mathematica. 110 (3): 407. doi:10.1007/s00229-002-0336-2. S2CID 121266346. Mori, Shigefumi (1982). "Threefolds Whose Canonical Bundles Are Not Numerically Effective". Annals of Mathematics. 116 (1): 133–176. doi:10.2307/2007050. JSTOR 2007050. Mori, Shigefumi (1988). "Flip theorem and the existence of minimal models for 3-folds". Journal of the American Mathematical Society. 1 (1): 117–253. doi:10.1090/S0894-0347-1988-0924704-X. JSTOR 1990969. Kollár, János; Miyaoka, Yoichi; Mori, Shigefumi. Rationally connected varieties. J. Algebraic Geom. 1 (1992), no. 3, 429–448. Kollár, János; Miyaoka, Yoichi; Mori, Shigefumi (1992). "Rational connectedness and boundedness of Fano manifolds". Journal of Differential Geometry. 36 (3). doi:10.4310/jdg/1214453188. S2CID 118102421. Kollár, János; Mori, Shigefumi (1992). "Classification of three-dimensional flips". Journal of the American Mathematical Society. 5 (3): 533–703. doi:10.1090/S0894-0347-1992-1149195-9. JSTOR 2152704. Keel, Sean; Mori, Shigefumi (1997). "Quotients by Groupoids". Annals of Mathematics. 145 (1): 193–213. arXiv:alg-geom/9508012. doi:10.2307/2951828. JSTOR 2951828. S2CID 17830187. Kollár, János; Mori, Shigefumi. Birational geometry of algebraic varieties. With the collaboration of C. H. Clemens and A. Corti. Translated from the 1998 Japanese original. Cambridge Tracts in Mathematics, 134. Cambridge University Press, Cambridge, 1998. viii+254 pp. ISBN 0-521-63277-3

Illustrations

Worked examples

Example 1 — a first encounter with Shigefumi Mori

Start with the simplest possible case. Write down what Shigefumi Mori claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Shigefumi Mori before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Shigefumi Mori ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Shigefumi Mori

In research: Shigefumi Mori appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Shigefumi Mori in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Shigefumi Mori is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1951 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Shigefumi Mori outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Shigefumi Mori in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Shigefumi Mori means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Shigefumi Mori out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Shigefumi Mori in simple terms?

Why does Shigefumi Mori matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Shigefumi Mori?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Shigefumi Mori.