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44 relations: Algebraic geometry, Algebraic geometry and analytic geometry, Ample line bundle, Analytic function, Bivector (complex), Bochner's formula, Calabi–Yau manifold, Cambridge University Press, Canonical bundle, Cartan's theorems A and B, Chern class, Complex analysis, Complex analytic space, Complex Lie group, Complex manifold, Complex projective space, Complex-analytic variety, Cousin problems, Divisor (algebraic geometry), Elsevier, Enriques–Kodaira classification, Eric Harold Neville, Formal sum, Harmonic analysis, Hartogs's extension theorem, Hermitian symmetric space, Hodge theory, Hopf manifold, John Wiley & Sons, Kähler manifold, Kobayashi metric, Kobayashi–Hitchin correspondence, Kodaira embedding theorem, Lelong number, List of complex and algebraic surfaces, Mathematics, Mirror symmetry (string theory), Morphism of algebraic varieties, Multiplier ideal, Picard group, Projective variety, Pseudoconvexity, Several complex variables, Stein manifold.
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Algebraic geometry and analytic geometry
In mathematics, algebraic geometry and analytic geometry are two closely related subjects.
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Ample line bundle
In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space.
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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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Bivector (complex)
In mathematics, a bivector is the vector part of a biquaternion.
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Bochner's formula
In mathematics, Bochner's formula is a statement relating harmonic functions on a Riemannian manifold (M, g) to the Ricci curvature.
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Calabi–Yau manifold
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Canonical bundle
In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n.
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Cartan's theorems A and B
In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf on a Stein manifold.
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Chern class
In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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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 Lie group
In geometry, a complex Lie group is a complex-analytic manifold that is also a group in such a way G \times G \to G, (x, y) \mapsto x y^ is holomorphic.
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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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Complex projective space
In mathematics, complex projective space is the projective space with respect to the field of complex numbers.
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Complex-analytic variety
In mathematics, specifically complex geometry, a complex-analytic variety is defined locally as the set of common zeros of finitely many analytic functions.
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Cousin problems
In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data.
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Divisor (algebraic geometry)
In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties.
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Elsevier
Elsevier is an information and analytics company and one of the world's major providers of scientific, technical, and medical information.
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Enriques–Kodaira classification
In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes.
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Eric Harold Neville
Eric Harold Neville, known as E. H. Neville (1 January 1889 London, England – 22 August 1961 Reading, Berkshire, England) was an English mathematician.
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Formal sum
In mathematics, a formal sum, formal series, or formal linear combination may be.
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Harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis).
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Hartogs's extension theorem
In mathematics, precisely in the theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several variables.
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Hermitian symmetric space
In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has as an inversion symmetry preserving the Hermitian structure.
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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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Hopf manifold
In complex geometry, a Hopf manifold is obtained as a quotient of the complex vector space (with zero deleted) (^n\backslash 0) by a free action of the group \Gamma \cong of integers, with the generator \gamma of \Gamma acting by holomorphic contractions.
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John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
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Kähler manifold
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure.
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Kobayashi metric
In mathematics and especially complex geometry, the Kobayashi metric is a pseudometric intrinsically associated to any complex manifold.
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Kobayashi–Hitchin correspondence
In differential geometry, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles.
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Kodaira embedding theorem
In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds.
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Lelong number
In mathematics, the Lelong number is an invariant of a point of a complex analytic variety that in some sense measures the local density at that point.
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List of complex and algebraic surfaces
This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to the Enriques–Kodaira classification.
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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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Mirror symmetry (string theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds.
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Morphism of algebraic varieties
In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.
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Multiplier ideal
In commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number c consists (locally) of the functions h such that is locally integrable, where the fi are a finite set of local generators of the ideal.
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Picard group
In mathematics, the Picard group of a ringed space X, denoted by Pic(X), is the group of isomorphism classes of invertible sheaves (or line bundles) on X, with the group operation being tensor product.
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Projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective ''n''-space Pn over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety.
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Pseudoconvexity
In mathematics, more precisely in the theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn.
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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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Stein manifold
In the theory of several complex variables and complex manifolds in mathematics, a Stein manifold is a complex submanifold of the vector space of n complex dimensions.
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Redirects here:
Complex analytic geometry, Complex analytical geometry, Geometry of Complex Numbers.
References
[1] https://en.wikipedia.org/wiki/Complex_geometry
