differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a complex manifold that allows the...

and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds...

Chow's theorem states that a projective complex analytic variety, i.e., a closed analytic subvariety of the complex projective space C P n {\displaystyle...

one whose first Chern class vanishes. Complex dimension Complex analytic variety Quaternionic manifold Real-complex manifold One must use the open unit...

study singular spaces in complex geometry, such as singular complex analytic varieties or singular complex algebraic varieties, whereas in differential...

complex-analytic variety. The most common example of a complete variety is a projective variety, but there do exist complete non-projective varieties...

n-tuples of complex numbers. The name of the field dealing with the properties of these functions is called several complex variables (and analytic space)...

is a space that is locally the same as an analytic variety. They are prominent in the study of several complex variables, but they also appear in other...

variety. Since analytic varieties may have singular points, not all complex analytic varieties are manifolds. Over a non-archimedean field analytic geometry...

geometry of projective complex varieties. For example, the theory of holomorphic vector bundles (more generally coherent analytic sheaves) on X coincide...

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic...

field of fractions. In complex geometry the objects of study are complex analytic varieties, on which we have a local notion of complex analysis, through which...

analytics, diagnostic analytics, predictive analytics, prescriptive analytics, and cognitive analytics. Analytics may apply to a variety of fields such as...

for abelian varieties of dimension d > 1. The problem is at a deeper level of abstraction, because it is much harder to manipulate analytic functions of...

Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on...

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. It...

dimension, codimension 1 boundary, codimension 2 corners), real or complex analytic varieties, or orbit spaces of smooth transformation groups. A Thom–Mather...

in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth projective algebraic variety that is also an algebraic...

Birational geometry Motive (algebraic geometry) Analytic variety Zariski–Riemann space Semi-algebraic set Fano variety Mnëv's universality theorem Hartshorne,...

real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds...

Look up analytic, analytical, or analyticity in Wiktionary, the free dictionary. Analytic or analytical may refer to: Analytical chemistry, the analysis...

and complex analytic varieties, and holomorphic vector bundles and coherent sheaves over these spaces. Special examples of spaces studied in complex geometry...

topological spaces considered are Riemann surfaces or more generally complex analytic varieties, germs of holomorphic functions on them can be viewed as power...

the Whitney conditions for subanalytic sets (such as real or complex analytic varieties). Verdier called the condition (w) for Whitney, as at the time...

of complex spaces, such as Stein manifolds, complex manifolds, or complex analytic varieties. Note that this theory can be globalized to complex manifolds...

Analytic journalism is a field of journalism that seeks to make sense of complex reality in order to create public understanding. It combines aspects of...

note that a real variety may be a manifold and have singular points. For example the equation y3 + 2x2y − x4 = 0 defines a real analytic manifold but has...

proper map between complex analytic spaces. Some authors call a proper variety over a field k {\displaystyle k} a complete variety. For example, every...

In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean field. Such spaces were introduced by John Tate...

in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties. In simple...