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Encyclopedia > Oscar Zariski

Oscar Zariski was one of the most influential mathematicians working in the field of algebraic geometry in the twentieth century. He was born as Ascher Zaritsky on 24 April 1899, in Kobrin (now in Belarus, then in Poland occupied by Russia) in a Jewish family. He died on 4 July 1986 in Brookline, Massachusetts. This article is in need of attention from an expert on the subject. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s The 20th century lasted from 1901 to 2000 in the Gregorian calendar (often from (1900 to 1999 in common usage). ... April 24 is the 114th day of the year in the Gregorian Calendar (115th in leap years). ... 1899 (MDCCCXCIX) was a common year starting on Sunday (see link for calendar). ... Kobrin (Belarusian: Ко́брынь, Ко́брын; Polish: Kobryń; Russian: Ко́брин) is a city in the Brest voblast of Belarus and the center of the Kobryn District. ... July 4 is the 185th day of the year (186th in leap years) in the Gregorian Calendar, with 180 days remaining. ... 1986 (MCMLXXXVI) is a common year starting on Wednesday of the Gregorian calendar. ... Official language(s) English Capital Boston Largest city Boston Area  - Total  - Width  - Length  - % water  - Latitude  - Longitude Ranked 44th 10,555 mi²; 27,360 km² 183 mi; 295 km 113 mi; 182 km 13. ...

He was a student at the University of Kiev in 1918, moving to Rome to study in 1920. He became a disciple of the Italian school of algebraic geometry, studying with Guido Castelnuovo, Federigo Enriques and Francesco Severi. He wrote a doctoral dissertation in 1924, on a topic in Galois theory. It was when it came to be published that he accepted a suggestion to change his name for professional purposes. Shevchenko Kyiv University in Kyiv is the largest and most important university of Ukraine. ... 1918 (MCMXVIII) was a common year starting on Tuesday of the Gregorian calendar (see link for calendar) or a common year starting on Wednesday of the Julian calendar. ... City motto: Senatus Populusque Romanus – SPQR (The Senate and the People of Rome) Founded 21 April 753 BC mythical, 1st millennium BC Region Latium Mayor Walter Veltroni (Left-Wing Democrats) Area  - City Proper  1285 km² Population  - City (2004)  - Metropolitan  - Density (city proper) 2. ... 1920 (MCMXX) was a leap year starting on Thursday (link will take you to calendar) // Events January January 7 - Forces of Russian White admiral Kolchak surrender in Krasnoyarsk. ... 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) done internationally in birational geometry, particularly on algebraic surfaces. ... Guido Castelnuovo (14 August 1865, Venice – 27 April 1952, Rome) 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 classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry. ... Franceso Severi (13 April 1879, Arezzo, Italy - 8 December 1961, Rome) was an Italian mathematician. ... 1924 (MCMXXIV) was a leap year starting on Tuesday (link will take you to calendar). ... In mathematics, Galois theory is a branch of abstract algebra. ...

He emigrated to the USA in 1927, supported by Solomon Lefschetz. He had a position at Johns Hopkins University, where he became professor in 1937. 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... Solomon Lefschetz (3 September 1884-5 October 1972) was a US mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations. ... The Johns Hopkins University is a private institution of higher learning located in Baltimore, Maryland, United States. ... 1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar). ...

It was this period that he wrote the celebrated book Algebraic Surfaces, intended as a summation of the work of the Italian school, but in effect its swansong, too. It was published in 1935. It was reissued many years later, with copious notes showing how much the field of algebraic geometry had changed, not only foundationally but in emphasis. It is still an important reference. 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ...

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). 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 only on its function field. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... This article needs to be cleaned up to conform to a higher standard of quality. ... In mathematics, a rational function is a ratio of polynomials. ... In mathematics, the term dense has at least three different meanings. ... Model Theory In logic and model theory, a valuation is a map from the set of variables of a first-order language to the universe of some interpretation of that language. ...

Zariski became professor at Harvard University in 1947, retiring in 1969. In 1945 he fruitfully discussed foundational matters for algebraic geometry with AndrĂ© 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. Harvard University is a private university in Cambridge, Massachusetts, USA and a member of the Ivy League. ... 1947 (MCMXLVII) was a common year starting on Wednesday (link will take you to calendar). ... 1969 (MCMLXIX) was a common year starting on Wednesday For other uses, see Number 1969. ... 1945 (MCMXLV) was a common year starting on Monday (link will take you to calendar). ... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ... In number theory, a local zeta-function is a generating function Z(t) for the number of solutions of a set of equations defined over a finite field F, in extension fields Fk of F. The analogy with the Riemann zeta function comes via consideration of the logarithmic derivative . ...

At Harvard, Zariski's students included Shreeram Abhyankar, Heisuke Hironaka, David Mumford and Michael Artin - 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. Shreeram Shankar Abhyankar (born 1930)is Marshall Distinguished Professor of Mathematics and Professor of Computer Science and Industrial Engineering at Purdue University, Indiana, USA. He earned his B.Sc. ... Heisuke Hironaka (広中 平祐 Hironaka Heisuke, born April 9, 1931) is a Japanese mathematician. ... David Bryant Mumford (born 11 June 1937) is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. ... Michael Artin is an American mathematician, known for his contributions to algebraic geometry. ... For non-mathematical singularity theories, see singularity. ... In algebraic geometry, the moduli problem is to describe the parameters on which algebraic varieties depend. ... Alexander Grothendieck (Berlin, March 28, 1928) was one of the most important mathematicians active in the 20th century. ...

He was awarded the Steele Prize in 1981. He wrote also Commutative Algebra in two volumes, with Pierre Samuel. His papers have been published by MIT Press, in four volumes. The Unreal Life of Oscar Zariski (1991) is a biography by Carol Ann Parikh. 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. ... 1981 (MCMLXXXI) is a common year starting on Thursday of the Gregorian calendar. ... Pierre Samuel was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. ... MIT Press Books The MIT Press is a university publisher affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts. ... 1991 (MCMXCI) is a common year starting on Tuesday of the Gregorian calendar. ...

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  Results from FactBites:
Oscar Zariski - definition of Oscar Zariski in Encyclopedia (582 words)
Oscar Zariski was one of the most influential mathematicians working in the field of algebraic geometry in the twentieth century.
The Zariski topology, as it was later known, is adequate for biregular geometry, where varieties are mapped by polynomial functions.
Zariski became professor at Harvard University in 1947, retiring in 1969.
Zariski topology - Wikipedia, the free encyclopedia (1433 words)
In mathematics, namely algebraic geometry, the Zariski topology is a particular topology chosen for algebraic varieties that reflects the algebraic nature of their definition but is only weakly related to their geometric properties; it is due to Oscar Zariski and took a place of particular importance in the field around 1950.
In this sense, the Zariski topology is an organizational tool rather than an object of study (compare with the role of the topology in algebraic topology).
This is one instance of the geometric unsuitability of the Zariski topology.
  More results at FactBites »



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