mathematics

Shigeru Mukai

Shigeru Mukai 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 Shigeru Mukai rather than just read about it. In short: Shigeru Mukai (向井茂, Mukai Shigeru; born 1953) is a Japanese mathematician at Kyoto University specializing in algebraic geometry. Work He introduced the Fourier–Mukai transform in 1981 in a paper on abelian varieties, which also made up his doctoral thesis.

Key takeaways

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

Reference excerpt

Shigeru Mukai (向井茂, Mukai Shigeru; born 1953) is a Japanese mathematician at Kyoto University specializing in algebraic geometry.

Work He introduced the Fourier–Mukai transform in 1981 in a paper on abelian varieties, which also made up his doctoral thesis. His research since has included work on vector bundles on K3 surfaces, three-dimensional Fano varieties, moduli theory, and non-commutative Brill–Noether theory. He also found a new counterexample to Hilbert's 14th problem (the first counterexample was found by Nagata in 1959).

Publications Mukai, Shigeru; Oxbury, W. M. (8 September 2003) [First published 1998], An Introduction to Invariants and Moduli, Cambridge Studies in Advanced Mathematics, vol. 81, Cambridge University Press, ISBN 978-0-521-80906-1, MR 2004218 Mukai, Shigeru (5 December 2008), モジュライ理論（1） [Moduli Theory (1)], Iwanami Shoten, ISBN 978-400006057-8 Mukai, Shigeru (5 December 2008), モジュライ理論（2） [Moduli Theory (2)], Iwanami Shoten, ISBN 978-400006058-5 Mukai, Shigeru (1981). "Duality between D ( X ) {\displaystyle D(X)} and D ( X ^ ) {\displaystyle D({\hat {X}})} with its application to Picard sheaves". Nagoya Mathematical Journal. 81: 153–175. doi:10.1017/S002776300001922X. ISSN 0027-7630.

References

External links Official website Shigeru Mukai at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Shigeru Mukai

Start with the simplest possible case. Write down what Shigeru Mukai 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 Shigeru Mukai 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 Shigeru Mukai 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 Shigeru Mukai

In research: Shigeru Mukai 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 Shigeru Mukai 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: Shigeru Mukai is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1953 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Shigeru Mukai 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 Shigeru Mukai in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Shigeru Mukai 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 Shigeru Mukai out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Shigeru Mukai in simple terms?

Shigeru Mukai (向井茂, Mukai Shigeru; born 1953) is a Japanese mathematician at Kyoto University specializing in algebraic geometry. Work He introduced the Fourier–Mukai transform in 1981 in a paper on abelian varieties, which also made up his doctoral thesis.

Why does Shigeru Mukai 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 Shigeru Mukai?

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 Shigeru Mukai.