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Heisuke Hironaka
is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry. Career Hironaka entered Kyoto University in 1949. After completing his undergraduate studies at Kyoto University, he received his Ph.D. in 1960 from Harvard University while under the direction of Oscar Zariski. Hironaka held teaching positions at Brandeis University from 1960-1963, Columbia University in 1964, and Kyoto University from 1975 to 1988. He was a professor of mathematics at Harvard University from 1968 until becoming ''emeritus'' in 1992 and was a president of Yamaguchi University from 1996 to 2002. Research In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero. This means that any algebraic variety can be replaced by (more precisely is birationally equivalent to) a similar variety which has no singularities. He also introduced Hironaka's example showing that a deformation of Kähler manifolds need ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yamaguchi, Yamaguchi
is the capital city of Yamaguchi Prefecture, Japan. The city was founded on April 10, 1929. As of February 1, 2010, the city had an estimated population of 198,971 and a population density of 194.44 persons per km². The total area is 1,023.31 km². Yamaguchi is home to the Buddhist temple, , with its five-story pagoda. Yamaguchi is served by Yamaguchi Ube Airport in nearby Ube. History Merger history *April 1, 1889: 40 towns were merged to form the town of Yamaguchi. *April 1, 1905: The village of Kami-unorei was merged into the town of Yamaguchi. *July 1, 1915: The village of Shimo-unorei was merged into the town of Yamaguchi. *April 10, 1929: The town of Yamaguchi absorbed the village of Yoshiki to create the city of Yamaguchi (1st Generation). *April 1, 1941: The village of Miyano was merged into the city of Yamaguchi. *April 1, 1944: The towns of Ogōri and Ajisu, and the villages of Hirakawa, Ōtoshi, Sue, Natajima, Aiofutajima, Kagawa and Sayama were merged with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legion Of Honour
The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon, Napoleon Bonaparte, it has been retained (with occasional slight alterations) by all later French governments and regimes. The order's motto is ' ("Honour and Fatherland"); its Seat (legal entity), seat is the Palais de la Légion d'Honneur next to the Musée d'Orsay, on the left bank of the Seine in Paris. The order is divided into five degrees of increasing distinction: ' (Knight), ' (Officer), ' (Commander (order), Commander), ' (Grand Officer) and ' (Grand Cross). History Consulate During the French Revolution, all of the French Order of chivalry, orders of chivalry were abolished and replaced with Weapons of Honour. It was the wish of Napoleon, Napoleon Bonaparte, the French Consulate, First Consul, to create a reward to commend c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hironaka's Example
In geometry, Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds found by . Hironaka's example can be used to show that several other plausible statements holding for smooth varieties of dimension at most 2 fail for smooth varieties of dimension at least 3. Hironaka's example Take two smooth curves ''C'' and ''D'' in a smooth projective 3-fold ''P'', intersecting in two points ''c'' and ''d'' that are nodes for the reducible curve C\cup D. For some applications these should be chosen so that there is a fixed-point-free automorphism exchanging the curves ''C'' and ''D'' and also exchanging the points ''c'' and ''d''. Hironaka's example ''V'' is obtained by gluing two quasi-projective varieties V_1 and V_2. Let V_1 be the variety obtained by blowing up P \setminus c along C and then along the strict transform of D, and let V_2 be the variety obtained by blowing up P\setminus d along ''D'' and then along the strict transform of ''C''. Since ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birational Equivalence
In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying Map (mathematics), mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles. Birational maps Rational maps A rational mapping, rational map from one variety (understood to be Irreducible component, irreducible) X to another variety Y, written as a dashed arrow , is defined as a algebraic geometry#Morphism of affine varieties, morphism from a nonempty open subset U \subset X to Y. By definition of the Zariski topology used in algebraic geometry, a nonempty open subset U is always dense in X, in fact the complement of a lower-dimensional subset. Concretely, a rational map can be written in coordinates using rational functions. Birational maps A birational map from ''X'' to ''Y'' is a ration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Variety
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly. For example, some definitions require an algebraic variety to be irreducible, which means that it is not the union of two smaller sets that are closed in the Zariski topology. Under this definition, non-irreducible algebraic varieties are called algebraic sets. Other conventions do not require irreducibility. The fundamental theorem of algebra establishes a link between algebra and geometry by showing that a monic polynomial (an algebraic object) in one variable with complex number coefficients is determined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resolution Of Singularities
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety ''V'' has a resolution, a non-singular variety ''W'' with a proper birational map ''W''→''V''. For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic ''p'' it is an open problem in dimensions at least 4. Definitions Originally the problem of resolution of singularities was to find a nonsingular model for the function field of a variety ''X'', in other words a complete non-singular variety ''X′'' with the same function field. In practice it is more convenient to ask for a different condition as follows: a variety ''X'' has a resolution of singularities if we can find a non-singular variety ''X′'' and a proper birational map from ''X′'' to ''X''. The condition that the map is proper is needed to exclude trivial solutions, such as taking ''X′'' to be the subvariety of non- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Point Of An Algebraic Variety
In the mathematical field of algebraic geometry, a singular point of an algebraic variety is a point that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined. In case of varieties defined over the reals, this notion generalizes the notion of local non-flatness. A point of an algebraic variety which is not singular is said to be regular. An algebraic variety which has no singular point is said to be non-singular or smooth. Definition A plane curve defined by an implicit equation :F(x,y)=0, where is a smooth function is said to be ''singular'' at a point if the Taylor series of has order at least at this point. The reason for this is that, in differential calculus, the tangent at the point of such a curve is defined by the equation :(x-x_0)F'_x(x_0,y_0) + (y-y_0)F'_y(x_0,y_0)=0, whose left-hand side is the term of degree one of the Taylor expansion. Thus, if this term is zero, the tangent may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yamaguchi University
is a national university in Yamaguchi Prefecture, Japan. It has campuses at the cities of Yamaguchi and Ube. History The root of the university was , a private school founded by Ueda Hōyō (, 1769–1853) in 1815. In 1863 the school became a han school of Chōshū Domain and was renamed Yamaguchi Meirinkan. After the Meiji Restoration it became a prefectural secondary school, and in 1894 it developed into , a national institute of higher education. It served as a preparatory course for the Imperial University. In February 1905 the school was reorganized into , the third national commercial college in Japan, after Tokyo (1887) and Kobe (1902). In 1944 the school was renamed Yamaguchi College of Economics. In 1949 Yamaguchi University was established by integrating six public (national and prefectural) schools in Yamaguchi Prefecture, namely, (Revived) Yamaguchi Higher School, Yamaguchi College of Economics, Ube Technical College, Yamaguchi Normal School, Yamaguchi Youth No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title the rank of the last office held". In some cases, the term is conferred automatically upon all persons who retire at a given rank, but in others, it remains a mark of distinguished service awarded selectively on retirement. It is also used when a person of distinction in a profession retires or hands over the position, enabling their former rank to be retained in their title, e.g., "professor emeritus". The term ''emeritus'' does not necessarily signify that a person has relinquished all the duties of their former position, and they may continue to exercise some of them. In the description of deceased professors emeritus listed at U.S. universities, the title ''emeritus'' is replaced by indicating the years of their appointmentsThe Protoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research Institute For Mathematical Sciences
The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. RIMS was founded in April 1963. List of directors * Masuo Fukuhara (1963.5.1 – 1969.3.31) * Kōsaku Yosida (1969.4.1 – 1972.3.31) * Hisaaki Yoshizawa (1972.4.1 – 1976.3.31) * Kiyoshi Itō (1976.4.1 – 1979.4.1) * Nobuo Shimada (1979.4.2 – 1983.4.1) * Heisuke Hironaka (1983.4.2 – 1985.1.30) * Nobuo Shimada (1985.1.31 – 1987.1.30) * Mikio Sato (1987.1.31 – 1991.1.30) * Satoru Takasu (1991.1.31 – 1993.1.30) * Huzihiro Araki (1993.1.31 – 1996.3.31) * Kyōji Saitō (1996.4.1 – 1998.3.31) * Masatake Mori (1998.4.1 – 2001.3.31) * Masaki Kashiwara (2001.4.1 – 2003.3.31) * Yōichirō Takahashi (2003.4.1 – 2007.3.31) * Masaki Kashiwara (2007.4.1 – 2009.3.31) * Shigeru Morishige (2009.4.1 – 2011.3.31) * Shigefumi Mori (2011.4.1 – 2014.3.31) * Shigeru Mukai (2014.4.1 – 2017.3.31) * Michio Yamada (2017.4.1 – present) Not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard College
Harvard College is the undergraduate college of Harvard University, an Ivy League research university in Cambridge, Massachusetts. Founded in 1636, Harvard College is the original school of Harvard University, the oldest institution of higher learning in the United States and among the most prestigious in the world. Part of the Faculty of Arts and Sciences, Harvard College is Harvard University's traditional undergraduate program, offering AB and SB degrees. It is highly selective, with fewer than five percent of applicants being offered admission in recent years. Harvard College students participate in more than 450 extracurricular organizations and nearly all live on campus—first-year students in or near Harvard Yard, and upperclass students in community-oriented "houses". History The school came into existence in 1636 by vote of the Great and General Court of the Massachusetts Bay Colony—though without a single building, instructor, or student. In 1638, the colleg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard Magazine
''Harvard Magazine'' is an independently edited magazine and separately incorporated affiliate of Harvard University. Aside from ''The Harvard Crimson'', it is the only publication covering the entire university, and also regularly distributed to all graduates, faculty and staff. It was founded in 1898 by alumni for alumni, with the mission of "keeping alumni of Harvard University connected to the university and to each other". One of the founders was the noted print journalist William Morton Fullerton. It has gone through three name changes - the original name was ''Harvard Bulletin'', it was changed in 1910 to ''Harvard Alumni Bulletin'', and in 1973 it got its current name, ''Harvard Magazine''. ''Harvard Magazine'' has a circulation of 258,000 among alumni, faculty and staff in the United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
