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42 relations: Abraham Seidenberg, Alexander Grothendieck, Alfred Tarski, Algebraic curve, Algebraic geometry, Algebraic variety, Algebraically closed field, American Mathematical Monthly, Analytic function, Analytic space, Annales de l'Institut Fourier, Characteristic (algebra), Coherent sheaf, Compact space, Complex analytic space, Complex manifold, Degree of a field extension, Function field of an algebraic variety, Fundamental group, Hodge theory, Holomorphic function, Jean-Pierre Serre, Kodaira vanishing theorem, Laurent series, Liouville's theorem (complex analysis), Mathematical logic, Mathematics, Meromorphic function, Oka coherence theorem, Permutation representation, Projective space, Ramification (mathematics), Riemann sphere, Riemann surface, Ringed space, Several complex variables, Sheaf (mathematics), Solomon Lefschetz, Strong topology, Topological space, Wei-Liang Chow, Zariski topology.
Abraham Seidenberg
Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician.
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Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
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Alfred Tarski
Alfred Tarski (January 14, 1901 – October 26, 1983), born Alfred Teitelbaum,School of Mathematics and Statistics, University of St Andrews,, School of Mathematics and Statistics, University of St Andrews.
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Algebraic curve
In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
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Algebraically closed field
In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Analytic space
An analytic space is a generalization of an analytic manifold that allows singularities.
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Annales de l'Institut Fourier
The Annales de l'Institut Fourier is a French mathematical journal publishing papers in all fields of mathematics.
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Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.
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Coherent sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Complex analytic space
In mathematics, a complex analytic space is a generalization of a complex manifold which allows the presence of singularities.
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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Degree of a field extension
In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension.
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Function field of an algebraic variety
In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.
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Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
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Hodge theory
In mathematics, Hodge theory, named after W. V. D. Hodge, uses partial differential equations to study the cohomology groups of a smooth manifold M. The key tool is the Laplacian operator associated to a Riemannian metric on M. The theory was developed by Hodge in the 1930s as an extension of de Rham cohomology.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Jean-Pierre Serre
Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.
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Kodaira vanishing theorem
In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero.
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Laurent series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.
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Liouville's theorem (complex analysis)
In complex analysis, Liouville's theorem, named after Joseph Liouville, states that every bounded entire function must be constant.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
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Oka coherence theorem
In mathematics, the Oka coherence theorem, proved by, states that the sheaf of holomorphic functions over a complex manifold is coherent.
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Permutation representation
In mathematics, the term permutation representation of a (typically finite) group G can refer to either of two closely related notions: a representation of G as a group of permutations, or as a group of permutation matrices.
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Projective space
In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.
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Ramification (mathematics)
In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign.
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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
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Ringed space
In mathematics, a ringed space can be equivalently thought of as either Ringed spaces appear in analysis as well as complex algebraic geometry and scheme theory of algebraic geometry.
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Several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions on the n-tuples of complex numbers.
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Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
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Solomon Lefschetz
Solomon Lefschetz (Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
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Strong topology
In mathematics, a strong topology is a topology which is stronger than some other "default" topology.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Wei-Liang Chow
Chow Wei-Liang (October 1, 1911, Shanghai – August 10, 1995, Baltimore) was a Chinese mathematician born in Shanghai, known for his work in algebraic geometry.
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Zariski topology
In algebraic geometry and commutative algebra, the Zariski topology is a topology on algebraic varieties, introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring a topological space, called the spectrum of the ring.
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Chow theorem, GAGA, GAGA principle, Geometrie Algebrique et Geometrie Analytique, Géometrie Algébrique et Géométrie Analytique, Lefschetz principle, Riemann existence theorem, Riemann's existence theorem.
References
[1] https://en.wikipedia.org/wiki/Algebraic_geometry_and_analytic_geometry
