mathematics

Henri Skoda

Henri Skoda 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 Henri Skoda rather than just read about it. In short: Henri Skoda (born 1945) is a French mathematician, specializing in the analysis of several complex variables. Skoda studied from 1964 at l'École normale supérieure and received there in 1967 his agrégation in mathematics.

Key takeaways

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

Reference excerpt

Henri Skoda (born 1945) is a French mathematician, specializing in the analysis of several complex variables. Skoda studied from 1964 at l'École normale supérieure and received there in 1967 his agrégation in mathematics. He received in 1972 his Ph.D. from the University of Nice Sophia Antipolis under André Martineau (primary advisor) and Pierre Lelong (secondary advisor) with thesis Étude quantitative des sous-ensembles analytiques de Cn et des idéaux de functions holomorphes. Skoda became a professor in Toulon and since 1976 has been a professor at the University of Paris VI. For many years he ran an analysis seminar with Pierre Lelong and Pierre Dolbeault. In 1978 Skoda received the Poncelet Prize and as an invited speaker at the International Congress of Mathematicians in Helsinki gave a talk Integral methods and zeros of holomorphic functions. His doctoral students include Jean-Pierre Demailly.

Selected publications "Sous-ensembles analytiques d'ordre fini ou infini dans Cn". Bulletin de la Société Mathématique de France. 100: 353–408. 1972. with Joël Briançon: "Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de Cn". Comptes Rendus de l'Académie des Sciences, Série A. 278: 949–951. 1974. MR 0340642. "Application des techniques L2 à la théorie des idéaux d'une algèbre de fonctions holomorphes avec poids". Annales Scientifiques de l'École Normale Supérieure. 5 (4). 1972. "Valeurs au bord pour les solutions de l'opérateur dn, et caractérisation des zéros des fonctions de la classe de Nevanlinna". Bulletin de la Société Mathématique de France. 104: 225–299. 1976. Skoda, Henri (1982). "Prolongement des courants, positifs, fermés de masse finie". Inventiones Mathematicae. 66 (3): 361–376. Bibcode:1982InMat..66..361S. doi:10.1007/bf01389217. S2CID 121894299. Skoda, H. (1977). "Fibrés holomorphes à base et à fibre de Stein". Inventiones Mathematicae. 43 (2): 97–107. Bibcode:1977InMat..43...97S. doi:10.1007/BF01390000. S2CID 121033608. "Morphismes surjectifs de fibrés vectoriels semi-positifs". Annales Scientifiques de l'École Normale Supérieure. 11 (4). 1978. "Solution à croissance du second problème de Cousin dans Cn". Annales de l'Institut Fourier. 21 (1). 1971. with J.-P. Demailly: Demailly, J. -P.; Skoda, H. (1980). "Relations entre les notions de positivités de P.A.Griffiths et de S.Nakano pour les fibrés vectoriels". Séminaire Pierre Lelong - Henri Skoda (Analyse) Années 1978/79. Lecture Notes in Mathematics. Vol. 822. Springer Berlin Heidelberg. pp. 304–309. doi:10.1007/BFb0097764. ISBN 978-3-540-10241-0. Skoda, Henri (1978). "Morphismes surjectifs et fibrés linéaires semi-positifs". Séminaire Pierre Lelong — Henri Skoda (Analyse) Année 1976/77. Lecture Notes in Mathematics. Vol. 694. Springer Berlin Heidelberg. pp. 290–324. doi:10.1007/BFb0063255. ISBN 978-3-540-09101-1. Skoda, Henri (1980). "Relèvement des sections globales dans les fibrés semi-positifs". Séminaire Pierre Lelong - Henri Skoda (Analyse) Années 1978/79. Lecture Notes in Mathematics. Vol. 822. Springer Berlin Heidelberg. pp. 259–303. doi:10.1007/BFb0097763. ISBN 978-3-540-10241-0.

See also Briancon–Skoda theorem Skoda–El Mir theorem

References

External links Conference in Complex Analysis in honor of Henri Skoda — Paris, september 12–16 2005, Institut Henri Poincaré

Worked examples

Example 1 — a first encounter with Henri Skoda

Start with the simplest possible case. Write down what Henri Skoda 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 Henri Skoda 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 Henri Skoda 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 Henri Skoda

In research: Henri Skoda 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 Henri Skoda 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: Henri Skoda is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century French mathematicians, 21st-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henri Skoda 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 Henri Skoda in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henri Skoda means in your own words.
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Frequently asked questions

What is Henri Skoda in simple terms?

Why does Henri Skoda 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 Henri Skoda?

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 Henri Skoda.