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Scorza Variety
In mathematics, a ''k''-Scorza variety is a smooth projective variety, of maximal dimension among those whose ''k''–1 secant varieties are not the whole of projective space. Scorza varieties were introduced and classified by , who named them after Gaetano Scorza. The special case of 2-Scorza varieties are sometimes called Severi varieties, after Francesco Severi. Classification Zak showed that ''k''-Scorza varieties are the projective varieties of the rank 1 matrices of rank ''k'' simple Jordan algebras. Severi varieties The Severi varieties are the non-singular varieties of dimension ''n'' (even) in P''N'' that can be isomorphically projected to a hyperplane and satisfy ''N''=3''n''/2+2. *Severi showed in 1901 that the only Severi variety with ''n''=2 is the Veronese surface in P5. *The only Severi variety with ''n''=4 is the Segre embedding of P2×P2 into P8, found by Scorza in 1908. *The only Segre variety with ''n''=8 is the 8-dimensional Grassmannian ''G''(1,5) of lines in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaetano Scorza
Bernardino Gaetano Scorza (29 September 1876, in Morano Calabro – 6 August 1939, in Rome) was an Italian mathematician working in algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ..., whose work inspired the theory of Scorza varieties. Publications * * * References * {{DEFAULTSORT:Scorza, Gaetano Italian mathematicians People from the Province of Cosenza 1876 births 1939 deaths ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francesco Severi
Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematician. He was the chair of the committee on Fields Medal on 1936, at the first delivery. Severi was born in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables. He became the effective leader of the Italian school of algebraic geometry. Together with Federigo Enriques, he won the '' Bordin prize'' from the French Academy of Sciences. He contributed in a major way to birational geometry, the theory of algebraic surfaces, in particular of the curves lying on them, the theory of moduli spaces and the theory of functions of several complex variables. He wrote prolifically, and some of his work (following the intuition-led approach of Federigo Enriques) has subsequently been shown to be not rigorous according to the then new standards set in particular by Oscar Zariski and Andre Weil. Although many of his arguments have since ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Algebra
In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: # xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (). The product of two elements ''x'' and ''y'' in a Jordan algebra is also denoted ''x'' ∘ ''y'', particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative, meaning that x^n = x \cdots x is independent of how we parenthesize this expression. They also imply that x^m (x^n y) = x^n(x^m y) for all positive integers ''m'' and ''n''. Thus, we may equivalently define a Jordan algebra to be a commutative, power-associative algebra such that for any element x, the operations of multiplying by powers x^n all commute. Jordan algebras were first introduced by to formalize the notion of an algebra of observables in quantum mechanics. They were originally called "r-number systems", but were renamed "Jordan algebras" by , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Veronese Surface
In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics. It is named after Giuseppe Veronese (1854–1917). Its generalization to higher dimension is known as the Veronese variety. The surface admits an embedding in the four-dimensional projective space defined by the projection from a general point in the five-dimensional space. Its general projection to three-dimensional projective space is called a Steiner surface. Definition The Veronese surface is the image of the mapping :\nu:\mathbb^2\to \mathbb^5 given by :\nu: :y:z\mapsto ^2:y^2:z^2:yz:xz:xy/math> where :\cdots/math> denotes homogeneous coordinates. The map \nu is known as the Veronese embedding. Motivation The Veronese surface arises naturally in the study of conics. A conic is a degree 2 plane curve, thus defined by an equation: :Ax^2 + Bxy + Cy^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Segre Embedding
In mathematics, the Segre embedding is used in projective geometry to consider the cartesian product (of sets) of two projective spaces as a projective variety. It is named after Corrado Segre. Definition The Segre map may be defined as the map :\sigma: P^n \times P^m \to P^\ taking a pair of points ( \in P^n \times P^m to their product :\sigma:( _0:X_1:\cdots:X_n _0:Y_1:\cdots:Y_m \mapsto _0Y_0: X_0Y_1: \cdots :X_iY_j: \cdots :X_nY_m (the ''XiYj'' are taken in lexicographical order). Here, P^n and P^m are projective vector spaces over some arbitrary field, and the notation : _0:X_1:\cdots:X_n is that of homogeneous coordinates on the space. The image of the map is a variety, called a Segre variety. It is sometimes written as \Sigma_. Discussion In the language of linear algebra, for given vector spaces ''U'' and ''V'' over the same field ''K'', there is a natural way to map their cartesian product to their tensor product. : \varphi: U\times V \to U\otimes V.\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Greenlees Semple
John Greenlees Semple (10 June 1904 in Belfast, Ireland – 23 October 1985 in London, England) was a British mathematician working in algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical .... Publications * *Algebraic Projective Geometry. By J. G. Semple and G. T. Kneebone. Pp. viii, 404. 35s. 1952. (Oxford University Press). References * 20th-century British mathematicians Scientists from Belfast Mathematicians from Northern Ireland 1904 births 1985 deaths {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Lazarsfeld
Robert Kendall Lazarsfeld (born April 15, 1953) is an American mathematician, currently a professor at Stony Brook University. He was previously the Raymond L. Wilder Collegiate Professor of Mathematics at the University of Michigan. He is the son of two sociologists, Paul Lazarsfeld and Patricia Kendall. His research focuses on algebraic geometry. During 2002–2009, Lazarsfeld was an editor at the '' Journal of the American Mathematical Society'' (Managing Editor, 2007–2009). In 2012–2013, he served as the Managing Editor of the ''Michigan Mathematical Journal''. Lazarsfeld went to Harvard for undergraduate studies and earned his doctorate from Brown University in 1980 under supervision of William Fulton. In 2006 Lazarsfeld was elected a Fellow of the American Academy of Arts and Sciences. In 2012 he became a fellow of the American Mathematical Society. In 2015 he was awarded the AMS Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *''Memoirs of the American Mathematical Society'' *''Notices of the American Mathematical Society'' *'' Proceedings of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
