Oscar Zariski

Oscar Zariski
Oscar Zariski

Oscar Zariski (1899–1986)
Born April 24, 1899(1899-04-24)
Kobrin, Russian Empire
Died July 4, 1986(1986-07-04) (aged 87)
Brookline, Massachusetts
Nationality American
Fields Mathematics
Institutions Johns Hopkins University
University of Illinois
Harvard University
Alma mater University of Rome
University of Kiev
Doctoral advisor Guido Castelnuovo
Doctoral students S. S. Abhyankar
Michael Artin
Iacopo Barsotti
Irvin Cohen
Daniel Gorenstein
Robin Hartshorne
Heisuke Hironaka
Steven Kleiman
Joseph Lipman
David Mumford
Maxwell Rosenlicht
Pierre Samuel
Abraham Seidenberg
Known for Algebraic geometry
Notable awards Wolf Prize in Mathematics, Steele Prize

Oscar Zariski (born Oscher Zaritsky April 24, 1899, in Kobrin, Russian Empire (today Belarus), died July 4, 1986, Brookline, Massachusetts) was a Russian mathematician and one of the most influential algebraic geometers of the 20th century.



Zariski was born Oscher (also transliterated as Ascher or Osher) Zaritsky to a Jewish family (his parents were Bezalel Zaritsky and Hanna Tennenbaum) and in 1918 studied at the University of Kiev. He left Kiev in 1920 to study in Rome where he became a disciple of the Italian school of algebraic geometry, studying with Guido Castelnuovo, Federigo Enriques and Francesco Severi.

Zariski wrote a doctoral dissertation in 1924 on a topic in Galois theory. At the time of his dissertation publication, he changed his name for professional purposes to Oscar Zariski.

Johns Hopkins University years

Zariski emigrated to the United States in 1927 supported by Solomon Lefschetz. He had a position at Johns Hopkins University where he became professor in 1937. During this period, he wrote Algebraic Surfaces as a summation of the work of the Italian school. The book was published in 1935 and reissued 36 years later, with detailed notes by Zariski's students that illustrated how the field of algebraic geometry had changed. It is still an important reference.

It seems to have been this work that set the seal of Zariski's discontent with the approach of the Italians to birational geometry. The question of rigour he addressed by recourse to commutative algebra. The Zariski topology, as it was later known, is adequate for biregular geometry, where varieties are mapped by polynomial functions. That theory is too limited for algebraic surfaces, and even for curves with singular points. A rational map is to a regular map as a rational function is to a polynomial: it may be indeterminate at some points. In geometric terms, one has to work with functions defined on some open, dense set of a given variety. The description of the behaviour on the complement may require infinitely near points to be introduced to account for limiting behaviour along different directions. This introduces a need, in the surface case, to use also valuation theory to describe the phenomena such as blowing up (balloon-style, rather than explosively).

Harvard University years

After spending a year 1946–1947 at the University of Illinois, Zariski became professor at Harvard University in 1947 where he remained until his retirement in 1969. In 1945, he fruitfully discussed foundational matters for algebraic geometry with André Weil. Weil's interest was in putting an abstract variety theory in place, to support the use of the Jacobian variety in his proof of the Riemann hypothesis for curves over finite fields, a direction rather oblique to Zariski's interests. The two sets of foundations weren't reconciled at that point.

At Harvard, Zariski's students included Shreeram Abhyankar, Heisuke Hironaka, David Mumford, Michael Artin and Steven Kleiman — thus spanning the main areas of advance in singularity theory, moduli theory and cohomology in the next generation. Zariski himself worked on equisingularity theory. Some of his major results, Zariski's main theorem and the Zariski theorem on holomorphic functions, were amongst the results generalized and included in the programme of Alexander Grothendieck that ultimately unified algebraic geometry.

Zariski proposed the first example of a Zariski surface in 1958.

Awards and recognition

Zariski was awarded the Steele Prize in 1981, and in the same year the Wolf Prize in Mathematics with Lars Ahlfors. He wrote also Commutative Algebra in two volumes, with Pierre Samuel. His papers have been published by MIT Press, in four volumes.

See also



External links

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Oscar Zariski — Oscar Zariski, geboren als Ascher Zaritsky, (* 24. April 1899, in Kobryn, Weißrussland; † 4. Juli 1986 in Brookline, Massachusetts, USA) war ein US amerikanischer Mathematiker, der wichtige Beiträge zur Grundlegung der …   Deutsch Wikipedia

  • Oscar Zariski — Naissance 24 avril 1899 Kobrin (  Em …   Wikipédia en Français

  • Oscar Zariski — (Kobrin, 24 de abril de 1899 Brookline, Massachusetts, 4 de julio de 1986) fue un matemático estadounidense de origen polaco. Carrera Estudió en la Universidad de Kiev, ob …   Wikipedia Español

  • Zariski — Oscar Zariski Oscar Zariski, geboren als Ascher Zaritsky, (* 24. April 1899, in Kobryn, Weißrussland; † 4. Juli 1986 in Brookline, Massachusetts, USA) war ein US amerikanischer Mathematiker, der wichtige Beiträge zur Grundlegung der …   Deutsch Wikipedia

  • ZARISKI (O.) — ZARISKI OSCAR (1899 1986) Mathématicien américain d’origine russe, né à Kobrin, près de Brest. Oscar Zariski a contribué de façon importante à l’essor de la géométrie algébrique moderne. Après des études supérieures à l’université de Kiev,… …   Encyclopédie Universelle

  • Zariski surface — In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p gt; 0 such that there is a dominant inseparable map of degree p from the projective plane to the surface. In particular, all Zariski… …   Wikipedia

  • Zariski topology — In algebraic geometry, the Zariski topology is a particular topology chosen for algebraic varieties that reflects the algebraic nature of their definition. It is due to Oscar Zariski and took a place of particular importance in the field around… …   Wikipedia

  • Zariski-Topologie — Die Zariski Topologie ist ein Begriff aus dem mathematischen Teilgebiet der algebraischen Geometrie. Sie ist die natürliche Topologie auf den Studienobjekten der algebraischen Geometrie, den algebraischen Varietäten oder allgemeiner den Schemata …   Deutsch Wikipedia

  • Óscar (nombre) — Para otros usos de este término, véase Oscar (desambiguación). Óscar u Oscar Oscar Wilde Origen germano …   Wikipedia Español

  • ZARISKI, OSCAR — (1899–1986), U.S. mathematician. Zariski was born in Kobrin, Russia, His father was a talmudic scholar who died when Zariski was two, leaving his mother Hannah to support seven children. She did this by running a store, and in fact the family… …   Encyclopedia of Judaism

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.