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Oscar Zariski (born Oscher Zaritsky 24 April 1899 in Kobrin, Poland (today Belarus), died 4 July 1986 (Brookline, Massachusetts) was a Belarusian-American mathematician and one of the most influential algebraic geometers of the 20th century. Events 1479 BC - Thutmose III ascends to the throne of Egypt, although power effectively shifts to Hatshepsut (according to Year 1899 ( MDCCCXCIX) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common Kobryn or Kobrin (Ко́брын 'kɔbrɨn קאברין Kobryń Ко́брин is a city in the Brest voblast of Belarus and the center of the Poland (Polska officially the Republic of Poland Belarus ( Belarusian Беларусь / Biełaruś is a Landlocked country in Eastern Europe, bordered by Russia to the north and east Events 836 - Pactum Sicardi, peace between the Principality of Benevento and the Duchy of Naples Year 1986 ( MCMLXXXVI) was a Common year starting on Wednesday (link displays 1986 Gregorian calendar) Brookline is a town in Norfolk County, Massachusetts, United States, which borders on the cities of Boston and Newton. A mathematician is a person whose primary area of study and research is the field of Mathematics. Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with The twentieth century of the Common Era began on

Contents

Education

Zariski was born Osher Zaritsky to a Jewish family and in 1918 studied at the University of Kiev. Year 1918 ( MCMXVIII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common Kiev University or officially the National Taras Shevchenko University of Kyiv (Київський національний університет ім 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. Rome ( Roma ˈroma Roma is the capital city of Italy and Lazio, and is Italy's largest and most populous city with more than 2 In relation with the history of Mathematics, the Italian school of Algebraic geometry refers to the work over half a century or more (flourishing roughly 1885-1935 Guido Castelnuovo ( 14 August 1865 &ndash 27 April 1952 was an Italian Jewish Mathematician. Federigo Enriques ( 5 January 1871 – 14 June 1946) was an Italian mathematician now known principally as the first to give a Francesco Severi ( 13 April 1879, Arezzo, Italy - 8 December 1961, Rome) was an Italian Mathematician

Zaritsky wrote a doctoral dissertation in 1924 on a topic in Galois theory. In Mathematics, more specifically in Abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field 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 USA in 1927 supported by Solomon Lefschetz. The United States of America —commonly referred to as the Solomon Lefschetz ( 3 September 1884 – 5 October 1972) was an American Mathematician who did fundamental work on 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 years later, with detailed notes that illustrated how the field of algebraic geometry had changed, and 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. In Mathematics, birational geometry is a part of the subject of Algebraic geometry, that deals with the geometry of an Algebraic variety that is dependent The question of rigour he addressed by recourse to commutative algebra. Commutative algebra is the branch of Abstract algebra that studies Commutative rings their ideals, and modules over such rings The Zariski topology, as it was later known, is adequate for biregular geometry, where varieties are mapped by polynomial functions. In Mathematics, namely Algebraic geometry, the Zariski topology is a particular Topology chosen for algebraic varieties that reflects the algebraic 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 Mathematics, a rational function is any function which can be written as the Ratio of two Polynomial functions Definitions In 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. In Mathematics, the notion of infinitely near points was initially part of the intuitive foundations of Differential calculus. 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). Valuation in mathematics may refer to Valuation (algebra Valuation (logic Valuation (measure theory In Mathematics, blowing up or blowup is a type of geometric modification particularly applied in Algebraic geometry, where it is essential in

Harvard University years

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. André Weil should not be confused with two other mathematicians with similar names Hermann Weyl (1885-1955 who made substantial contributions 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. In Number theory, a local zeta-function is a Generating function Z ( t) for the number of solutions of a set of equations 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. Shreeram Shankar Abhyankar was born in 1930 and is an Indian Mathematician known for his contributions to Algebraic geometry. Heisuke Hironaka (広中 平祐 Hironaka Heisuke; born April 9, 1931) is a Japanese Mathematician. David Bryant Mumford (born 11 June 1937) is a Mathematician known for distinguished work in Algebraic geometry, and then for research into Michael Artin (born 1934 is an American Mathematician and a professor at MIT, known for his contributions to Algebraic Steven Lawrence Kleiman (born 31 March 1942) is an American Mathematician. For other mathematical uses see Mathematical singularity. For non-mathematical uses see Gravitational singularity. In Algebraic geometry, a moduli space is a geometric space (usually a scheme or an Algebraic stack) whose points represent algebro-geometric objects of 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. Experimental infobox see Wikipedia talkPersondata before changing --> Alexander Grothendieck (born March 28, 1928 in Berlin, Germany

Zariski proposed the first example of a Zariski surface in 1958. In Algebraic geometry, a branch of Mathematics, a Zariski surface is a Surface over a field of characteristic p  > 0 such

Awards and recognition

Zariski was awarded the Steele Prize in 1981. The Leroy P Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of Mathematics. He wrote also Commutative Algebra in two volumes, with Pierre Samuel. Pierre Samuel (born 12 September 1921 in Paris) is a French mathematician known for his work in Commutative algebra and its applications His papers have been published by MIT Press, in four volumes. The MIT Press is a University press affiliated with the Massachusetts Institute of Technology (MIT in Cambridge Massachusetts ( USA)

Sources

The Unreal Life of Oscar Zariski (1991) is a biography by Carol Ann Parikh. Another biography of Oscar Zariski appeared in the Gazette of the Australian Mathematical Society in the period 1988-1991, authorized by his wife Yole Zariski.

See also

External links

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