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General Elephant
In algebraic geometry, ''general elephant'' is an idiosyncratic name for a general element of the anticanonical system of a variety, introduced by Miles Reid Miles Anthony Reid FRS (born 30 January 1948) is a mathematician who works in algebraic geometry. Education Reid studied the Cambridge Mathematical Tripos at Trinity College, Cambridge and obtained his Ph.D. in 1973 under the supervision of .... For 3-folds the general elephant problem (or conjecture) asks whether general elephants have at most du Val singularities; this has been proved in several cases. References * Algebraic geometry {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miles Reid
Miles Anthony Reid FRS (born 30 January 1948) is a mathematician who works in algebraic geometry. Education Reid studied the Cambridge Mathematical Tripos at Trinity College, Cambridge and obtained his Ph.D. in 1973 under the supervision of Peter Swinnerton-Dyer and Pierre Deligne. Career Reid was a research fellow of Christ's College, Cambridge from 1973 to 1978. He became a lecturer at the University of Warwick in 1978 and was appointed professor there in 1992. He has written two well known books: ''Undergraduate Algebraic Geometry'' and ''Undergraduate Commutative Algebra''. Awards and honours Reid was elected a Fellow of the Royal Society in 2002. In the same year, he participated as an Invited Speaker in the International Congress of Mathematicians in Beijing. Reid was awarded the Senior Berwick Prize in 2006 for his paper with Alessio Corti and Aleksandr Pukhlikov, "Fano 3-fold hypersurfaces", which made a big advance in the study of 3-dimensional algebraic variet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Du Val Singularities
In algebraic geometry, a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex surface which is modeled on a double branched cover of the plane, with minimal resolution obtained by replacing the singular point with a tree of smooth rational curves, with intersection pattern dual to a Dynkin diagram of A-D-E singularity type. They are the canonical singularities (or, equivalently, rational Gorenstein singularities) in dimension 2. They were studied by Patrick du Val and Felix Klein. The Du Val singularities also appear as quotients of \Complex^2 by a finite subgroup of SL2(\Complex); equivalently, a finite subgroup of SU(2), which are known as binary polyhedral groups. The rings of invariant polynomials of these finite group actions were computed by Klein, and are essentially the coordinate rings of the singularities; this is a classic result in invariant theory. Classification The ... [...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 became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over 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 influentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
