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Heisuke Hironaka

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9 April 1931

Yamaguchi-ken, Japan

Presentation Wikipedia
Heisuke Hironaka attended Kyoto University. This university was founded in 1897 to train small numbers of selected students as academics. By the time Hironaka entered Kyoto University, after World War II, it had been integrated into a mass higher education system but had maintained its prestige.

From Kyoto University Hironaka went to the United States where he continued his studies at Harvard. After completing his studies there, Hironaka was appointed to the staff at Harvard.

In 1970 Hironaka had the distinction of being awarded a Fields Medal at the International Congress at Nice. This was for his work on algebraic varieties which we describe below. Among the many other honours he has received is the Order of Culture from Japan in 1975.

Two algebraic varieties are said to be equivalent if there is a one-to-one correspondence between them with both the map and its inverse regular. Two varieties U and V are said to be birationally equivalent if they contain open sets U' and V' that are in biregular correspondence. Classical algebraic geometry studies properties of varieties which are invariant under birational transformations. Difficulties that arise as a result of the presence of singularities are avoided by using birational correspondences instead of biregular ones. The main problem in this area is to find a nonsingular algebraic variety U, that is birationally equivalent to an irreducible algebraic variety V, such that the mapping f: U V is regular but not biregular.

Hironaka gave a general solution of this problem in any dimension in 1964. His work generalised that of Zariski who had proved the theorem concerning the resolution of singularities on an algebraic variety for dimension not exceeding 3.

Source:School of Mathematics and Statistics University of St Andrews, Scotland