Oscar Zariski

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Oscar Zariski

Oscar Zariski , born as Ascher Zaritsky, (born April 24, 1899 , in Kobryn , Belarus ; † July 4, 1986 in Brookline , Massachusetts , USA ) was an American mathematician who made important contributions to the foundation of algebraic geometry .


He was born as the son of a Talmudic scholar under the name Ascher Zaritsky in 1899 in the Russian Empire (now Belarus ). His father died when he was two years old, and his mother Hannah raised the seven children as a shop owner. She was so successful at it that the family was soon among the richest in town.

In 1918 he began his mathematics studies in Kiev in the middle of the civil war riots - he was even shot once - and continued this in 1920 in Rome with Francesco Severi , Guido Castelnuovo and Federigo Enriques , the heads of the Italian school of algebraic geometry. In 1924 he received his doctorate and chose the name under which he is known today for this and for his future publications. In the same year he married the Italian literature student Yole Cagli, and a year later they had their first child. As a socialist he did not want to stay in fascist Italy and did not get a visa for Russia, he went to the USA in 1927 and, on the recommendation of Solomon Lefschetz, accepted a position at the Johns Hopkins University in Baltimore . There he had a difficult position and a large number of teaching staff. He did not become a professor until 1937.

In 1939 he received a Guggenheim Fellowship , which released him from his unloved position in Baltimore. This was followed by traveling and teaching at Caltech , at Harvard University (1950/51) and in São Paulo in Brazil, where he discussed the foundations of algebraic geometry with André Weil . From 1947 until his retirement in 1969 he was a professor at Harvard University.


In 1935 Zariski wrote a book on algebraic surfaces that summarized the results of the Italian school and, with its appendices in the later editions, makes the development of the area clear. Since then he was dissatisfied with the often vague (not "mathematically strict") methods of the Italian school and therefore strived for a purely algebraic foundation of the theory with commutative algebra , which had since been developed by Emmy Noether and Wolfgang Krull . Zariski attended Emmy Noether lectures at Princeton and saw the importance of Krull's theory of local rings . At about the same time, van der Waerden and André Weil (the latter with number-theoretic ulterior motives) tried to place algebraic geometry on a stricter basis. These approaches are now combined in Grothendieck's version of algebraic geometry. In this context, the Zariski topology is named after Zariski , in which closed sets are defined as sets of zeros of polynomials.

Zariski also worked on the resolution of singularities of algebraic varieties . His students Shreeram Abhyankar and Heisuke Hironaka also achieved fundamental results here (the latter proved the solvability for every dimension over fields of the characteristic 0, i.e. the complex and real numbers).

His students included important algebraic geometers such as Shreeram Abhyankar , Heisuke Hironaka (Fields Medal), David Mumford (Fields Medal), Robin Hartshorne , Steven Kleiman , Joseph Lipman and Michael Artin . He aligned his “school” with Alexander Grothendieck's regular guest professorships at Harvard.

Honors and Membership

1944 he received the Frank Nelson Cole Prize for algebra of the American Mathematical Society awarded. In the same year he was elected to the National Academy of Sciences , in 1948 Zariski became a member of the American Academy of Arts and Sciences and in 1951 the American Philosophical Society . From 1969 to 1970 he was President of the American Mathematical Society. In 1981 he received the Leroy P. Steele Prize of the American Mathematical Society and the Wolf Prize in Mathematics. In 1950 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge (Massachusetts) (The fundamental ideas of abstract algebraic geometry).


  • Collected papers , 4 vols., MIT press 1972–1979 (Eds. Hironaka, Mumford, Lipman, Bernard Teissier, forewords by Zariski)
  • with Pierre Samuel Commutative algebra , 2 vols., van Nostrand 1958, 1960, as well as Springer, Graduate texts in mathematics
  • Algebraic surfaces , Springer 1935, 1971 (results of mathematics and their border areas), with appendices from Mumford, Lipman.
  • Theory and application of holomorphic functions on algebraic varieties over arbitrary ground fields , Memoirs American Mathematical Society 1951, 1990
  • Introduction to the theory of minimal models in the theory of algebraic surfaces , Math. Society of Japan 1958
  • The fundamental ideas of abstract algebraic geometry , ICM Cambridge 1950


  • Carol Ann Parikh The unreal life of Oscar Zariski , Academic Press, London, San Diego 1991
  • Hartshorne, Review of Parikhs Biographie, American Mathematical Monthly Vol. 99, 1992, p. 482
  • Hauser [Ed.] Resolution of singularities - a research textbook in honor of Oscar Zariski , Birkhäuser 2000 (with biography of Lipman), partly online here: [1]
  • Abhyankar Historical ramblings in algebraic geometry and related algebra , American Mathematical Monthly 1976
  • Mumford Oscar Zariski , Notices American Mathematical Society, 1986, p. 891
  • Silke Slembek Oskar Zariski and the emergence of modern algebraic geometry. Mainz, Strasbourg 2002 (dissertation)

Web links


  1. It belonged to Poland after the First World War .
  2. Like most of his relatives, she died in the Holocaust .
  3. Book of Members 1780 – present, Chapter Z. (PDF; 117 kB) In: American Academy of Arts and Sciences (amacad.org). Retrieved February 6, 2018 .
  4. ^ Member History: Oscar Zariski. American Philosophical Society, accessed November 19, 2018 .