Oscar Zariski
Oscar Zariski, born as Ascher Zaritsky, ( born April 24, 1899 in Kobryn, Belarus, † July 4, 1986 in Brookline, Massachusetts, United States ) was an American mathematician who made major contributions to the foundations of algebraic geometry made .
Life
He was born the son of a Talmudic scholar under the name Ascher Zaritsky 1899 in Russia (now Belarus ). His father died when he was two years old, and his mother, Hannah brought the 7 children by the shop owner. She is so successful that the family soon became one of the richest in the city.
In 1918 he began his studies of mathematics in Kiev in the midst of civil unrest - once he even shot - and put it in 1920 in Rome with Francesco Severi, Guido Castelnuovo and Federigo Enriques continued, the heads of the Italian school of algebraic geometry. In 1924 he received his doctorate and chose for it and for its future publications the name by which he is known today. In the same year he married the Italian literature student Yole Cagli, a year later they had their first child. Since he did not want to stay in Fascist Italy as a socialist and Russia got a visa, he went in 1927 to the United States and, on the recommendation of Solomon Lefschetz a job at Johns Hopkins University in Baltimore. There he had to fulfill a difficult position and a high teaching workload. It was not until 1937 professor.
In 1939 he received a Guggenheim Fellowship, which freed him from his unloved place in Baltimore. This was followed by travel and teaching activities at Caltech, Harvard University (1950 /51) and in São Paulo, Brazil, where he discussed the foundations of algebraic geometry with André Weil. 1947 until his retirement in 1969 he was a professor at Harvard University.
Services
1935 Zariski wrote a book on algebraic surfaces, which summarizes the results of the Italian school and makes it clear with its appendices in the later reissues the development of the area. Since then, he was dissatisfied with the often vague (not " mathematically rigorous " ) methods of the Italian school and therefore sought a purely algebraic foundation of the theory of commutative algebra with which had meanwhile been especially developed by Emmy Noether and Wolfgang Krull. Zariski attended lectures by Emmy Noether in Princeton and recognized the importance of Krull's theory of local rings. Around the same time trying to make (the latter with number-theoretic ulterior motives ) algebraic geometry for stricter basics also van der Waerden, and André Weil. These approaches are today united in Grothendieck 's version of algebraic geometry. After the Zariski Zariski topology is named in this context, are defined in the closed sets as zero sets of polynomials.
Zariski also worked on the resolution of singularities of algebraic varieties. Here also his students Shreeram Abhyankar and Hironaka Heisuke achieved fundamental results (the latter proved the solvability for each dimension over fields of characteristic 0, ie the complex and real numbers ).
His pupils included important algebraic geometers as Shreeram Abhyankar, Heisuke Hironaka ( Fields Medal ), David Mumford ( Fields Medal ), Robin Hartshorne, Steven Kleiman, Joseph Lipman and Michael Artin. He turned his "school" through regular visiting professor of Alexander Grothendieck at Harvard on the program.
Honors
1944 Frank Nelson Cole Prize for Algebra from the American Mathematical Society awarded him. 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 ).
Works
- Collected Papers, 4 vols, MIT press 1972-1979 (ed. Hironaka, Mumford, Lipman, Bernard Teissier, forewords by Zariski )
- Pierre Samuel Commutative algebra, 2 vols, van Nostrand 1958, 1960, and Springer, Graduate texts in mathematics
- Algebraic surfaces, Springer 1935, 1971 ( Results of mathematics and its applications ), with appendices by 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, Cambridge ICM 1950