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 (540 words) - 11:38, 12 October 2023
$#C+1 = 1 : ~/encyclopedia/old_files/data/A010/A.0100450 Abstract algebraic geometry
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8 KB (1,165 words) - 16:08, 1 April 2020
...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
.../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 (793 words) - 16:10, 1 April 2020
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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
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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 (548 words) - 06:26, 21 April 2024
...cal problem of the rationality or uni-rationality of the moduli variety of algebraic curves of genus $g$.
...an algebraically closed field $k$ has the structure of a quasi-projective algebraic variety $M_g$ (see [[#References|[3]]]–[[#References|[5]]]).
5 KB (777 words) - 22:00, 7 July 2014
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as a compact algebraic variety with the aid of Grassmann coordinates (cf. [[Exterior algebra|Exter
7 KB (1,104 words) - 19:42, 5 June 2020
A (real or complex) number having the property that any number does not change if zero is adde
...y be zero. Such elements are called [[zero divisor]]s. Fields, skew-fields and [[integral domain]]s do not have zero divisors.
3 KB (471 words) - 21:06, 3 January 2015
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A [[Kähler metric|Kähler metric]] on a [[Complex manifold|complex manifold]] (or orbifold) whose [[Ricci tensor|Ricci tensor]] $\operatorname
6 KB (832 words) - 16:09, 27 January 2024
...orem]]: Let $M$ and $N$ be two [[Differentiable manifold|$C^r$ manifolds]] and $f:M\to N$ a surjective $C^r$ map. If $r> \max \{0, \dim M - \dim N\}$, th
...also used. It refers to a "general" set of conditions which is consistent and is also such that every sentence from a specified set of sentences is decid
4 KB (704 words) - 11:07, 6 September 2013
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over the field of real or complex numbers is a mapping $ x \rightarrow x ^ {*} $
4 KB (550 words) - 22:13, 5 June 2020