 | This article includes a list ofgeneral references, butit lacks sufficient correspondinginline citations. Please help toimprove this article byintroducing more precise citations.(August 2025) (Learn how and when to remove this message) |
Oscar Zariski | |
|---|---|
 Oscar Zariski (1899–1986) | |
| Born | Russian:О́скар Зари́сский (1899-04-24)April 24, 1899 |
| Died | July 4, 1986(1986-07-04) (aged 87) Brookline, Massachusetts, U.S. |
| Alma mater | University of Kyiv University of Rome |
| Known for | Contributions toalgebraic geometry |
| Awards | Cole Prize in Algebra(1944) National Medal of Science(1965) Wolf Prize(1981) Steele Prize(1981) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Johns Hopkins University University of Illinois Harvard University |
| Thesis | Sopra una classe di equazioni algebriche contenenti linearmente un parametro e risolubili per radicali (1926)[1] |
| 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 |
Oscar Zariski (April 24, 1899 – July 4, 1986) was an Americanmathematician. The Russian-born scientist was one of the most influentialalgebraic geometers of the 20th century.
 | This sectiondoes notcite anysources. Please helpimprove this section byadding citations to reliable sources. Unsourced material may be challenged andremoved.(August 2025) (Learn how and when to remove this message) |
Zariski was born Osher (also transliterated as Ascher or Oscher) Zaritsky (Russian:Ошер Зарицкий) to a Jewish family of Bezalel Zaritsky and Hannanée Tennenbaum inKobrin, Russian Empire and in 1918 studied at theUniversity of Kiev. He left Kiev in 1920 to study at theUniversity of Rome where he became a disciple of theItalian school of algebraic geometry, studying withGuido Castelnuovo,Federigo Enriques andFrancesco Severi.
Zariski wrote a doctoral dissertation in 1924 on a topic inGalois theory, which was proposed to him byCastelnuovo. At the time of his dissertation publication, he changed his name to Oscar Zariski.
| This sectiondoes notcite anysources. Please helpimprove this section byadding citations to reliable sources. Unsourced material may be challenged andremoved.(August 2025) (Learn how and when to remove this message) |
Zariski emigrated to theUnited States in 1927 supported bySolomon Lefschetz. He had a position atJohns Hopkins University where he became professor in 1937. During this period, he wroteAlgebraic 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 tobirational geometry. He addressed the question of rigour by recourse tocommutative algebra. TheZariski topology, as it was later known, is adequate forbiregular 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 arational 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 requireinfinitely near points to be introduced to account for limiting behaviouralong different directions. This introduces a need, in the surface case, to use alsovaluation theory to describe the phenomena such asblowing up (balloon-style, rather than explosively).
| This sectiondoes notcite anysources. Please helpimprove this section byadding citations to reliable sources. Unsourced material may be challenged andremoved.(August 2025) (Learn how and when to remove this message) |
After spending a year 1946–1947 at theUniversity of Illinois at Urbana–Champaign, Zariski became professor atHarvard University in 1947 where he remained until his retirement in 1969. In 1945, he fruitfully discussed foundational matters for algebraic geometry withAndré Weil. Weil's interest was in putting an abstract variety theory in place, to support the use of theJacobian variety in his proof of theRiemann 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 includedShreeram Abhyankar,Heisuke Hironaka,David Mumford,Michael Artin andSteven Kleiman—thus spanning the main areas of advance insingularity theory,moduli theory andcohomology 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 ofAlexander Grothendieck that ultimately unified algebraic geometry.
Zariski proposed the first example of aZariski surface in 1958.
He wroteCommutative Algebra in two volumes, withPierre Samuel.
Zariski was aJewish atheist.[2]
Zariski was elected to the United StatesNational Academy of Sciences in 1944,[3] theAmerican Academy of Arts and Sciences in 1948,[4] and theAmerican Philosophical Society in 1951.[5]
He was offeredGuggenheim Fellowship in 1939.[6] U.S.National Medal of Science: 1965.
Zariski was awardedCole Prize in 1944, theSteele Prize in 1981, and theWolf Prize in Mathematics withLars Ahlfors in 1981.
During 1969–1970 he was President of theAmerican Mathematical Society.
His papers have been published byMIT Press, in four volumes. In 1997 a conference was held in his honor inObergurgl, Austria.[7][8]
{{citation}}: CS1 maint: postscript (link)[12]And yet it did, even though since moving into the boarding house he had become an atheist and most of his friends, including his best friend, were Russians.
