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An imbedding of an algebraic variety $ X $
5 KB (747 words) - 06:29, 30 May 2020
The classical polylogarithms are special functions of a complex variable $z$, defined by the series
for $z$ a complex number inside the unit disk and $n$ an integer at least equal to $1$. These functions satisfy the different
2 KB (237 words) - 19:07, 1 May 2023
A generalization of the concept of a non-singular [[Algebraic variety|algebraic variety]]. A [[Scheme|scheme]] $ X $
with its algebraic closure $ \overline{k} $
3 KB (541 words) - 07:00, 21 July 2024
[[Abstract algebraic geometry]] |
[[Algebraic homotopy]] |
5 KB (477 words) - 23:07, 8 March 2012
$#C+1 = 1 : ~/encyclopedia/old_files/data/A010/A.0100450 Abstract algebraic geometry
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8 KB (1,166 words) - 06:19, 21 July 2024
...re on analytically hyperbolic varieties|range of conjectures]] linking the geometry of varieties to their Diophantine properties.
...ariski closure]] of the union of the images of all non-trivial maps from [[algebraic group]]s into $V$. Lang conjectured that the complement of the special set
2 KB (277 words) - 18:16, 2 October 2023
algebraic subvarieties of $A^n$. If $X$ is an affine algebraic variety
(see [[Affine algebraic set|Affine algebraic set]]) in $A^n$, the [[induced topology]] on $X$ is also known as the Zaris
2 KB (304 words) - 20:50, 15 March 2023
...of complex numbers a non-singular algebraic variety has the structure of a complex [[Analytic manifold|analytic manifold]].
...is itself a smooth scheme. In general, if $Y$ is a smooth scheme over $k$ and $f : X \rightarrow Y$ is a [[Smooth morphism|smooth morphism]], then $x$ is
4 KB (596 words) - 13:44, 17 October 2019
.../encyclopedia/old_files/data/A012/A.0102450 Analytic surface (in algebraic geometry)
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8 KB (1,169 words) - 18:47, 5 April 2020
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...are topologically equivalent to a circle in the Euclidean plane, while the complex projective straight line is topologically equivalent to a two-dimensional s
2 KB (335 words) - 08:23, 6 June 2020
...index ([[signature]]) $\sigma(M)$ of a compact [[Kähler manifold]] $M$ of complex dimension $2n$ can be computed by the formula
...or]]). This was proved by W.V.D. Hodge [[#References|[2]]] for the de Rham complex
3 KB (413 words) - 08:52, 23 November 2023
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...ut the importance of this invariant in the theory of the classification of algebraic varieties.
5 KB (777 words) - 22:14, 5 June 2020
$#C+1 = 27 : ~/encyclopedia/old_files/data/A011/A.0101720 Algebraic varieties, arithmetic of,
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5 KB (794 words) - 18:12, 18 July 2024
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...f a complex Kähler manifold, and whose geometry is strongly related to the geometry of this manifold.
6 KB (953 words) - 12:29, 29 December 2021
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is the field of complex numbers, the analytic bundle is said to be holomorphic). The number $ n $
6 KB (951 words) - 06:45, 22 February 2022
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of an [[Algebraic variety|algebraic variety]] $ X $,
8 KB (1,076 words) - 07:58, 21 January 2024
...sisting of a single variety implies resolution of the singularities of $V$ and can be obtained from the local uniformization theorem in dimension $\leq3$.
...">[3]</TD> <TD valign="top"> W.V.D. Hodge, D. Pedoe, "Methods of algebraic geometry" , '''3''' , Cambridge Univ. Press (1954) {{MR|0061846}} {{ZBL|0055.38705}}
3 KB (440 words) - 14:25, 1 May 2014
A [[Kähler metric|Kähler metric]] on a [[Complex manifold|complex manifold]] (or orbifold) whose [[Ricci tensor|Ricci tensor]] $\operatorname
...cture is due to E. Calabi: Let $N$ be a compact connected complex manifold and $c _ { 1 } ( M ) _ { R }$ its first [[Chern class|Chern class]]; then
5 KB (811 words) - 13:36, 17 October 2019
A two digit MSC entry like 16 is allowed and automatically extended to 16-XX.<br />
This template is directly called by [[Template:MSC]] and by [[Template:MSCwiki8]].
5 KB (494 words) - 22:21, 4 December 2014
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...this concept reduces to the concept of a regular mapping (a submersion) of complex manifolds. A finitely-represented (local) morphism of schemes $ f: X \ri
3 KB (549 words) - 07:00, 21 July 2024