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and $ N $
6 KB (927 words) - 22:11, 5 June 2020
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A [[Hermitian metric|Hermitian metric]] on a [[Complex manifold|complex manifold]] whose fundamental form $ \omega $
4 KB (543 words) - 22:15, 5 June 2020
of sections; and
...sheaves. If $\cF$ and $\cS$ are coherent, then so are $\cF\otimes_\cO \cS$ and ${\rm Hom}_\cO(\cF,\cS)$
3 KB (497 words) - 13:34, 6 January 2022
...(over a field $k$) all irreducible components of which have dimension $n$, and which is defined by a homogeneous ideal $I$ in the ring $k[T_0,\dots,T_N]$,
...$X$ is a non-singular connected variety, and $k=\mathbf C$ is the field of complex numbers, then
2 KB (416 words) - 12:41, 19 August 2014
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of integers, the ring of integers of some algebraic number field, the field $ \mathbf R $
4 KB (512 words) - 10:59, 29 May 2020
A complex (sometimes, real) number that is a root of a polynomial
...ynomial $x^2+1$, while $2^{1/n}$, where $n$ is any positive integer, is an algebraic number of degree $n$, being a root of the irreducible polynomial $x^n-2$.
10 KB (1,645 words) - 17:08, 14 February 2020
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sheeted covering surface over the Riemann sphere, extended over all finite and infinitely-distant branch points of $ S $.
1 KB (165 words) - 06:29, 30 May 2020
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A semi-algebraic set in $ \mathbf R ^ {n} $ (or $ k ^ {n} $,
4 KB (573 words) - 18:05, 26 January 2022
...encyclopedia/old_files/data/I050/I.0500320 Implicit function (in algebraic geometry)
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5 KB (768 words) - 22:11, 5 June 2020
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''of an algebraic variety''
3 KB (388 words) - 17:12, 7 February 2021
$#C+1 = 57 : ~/encyclopedia/old_files/data/C024/C.0204160 Complex space,
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5 KB (691 words) - 17:46, 4 June 2020
The divisor class group under algebraic equivalence on a non-singular projective variety.
...ent group $D(X)/D_{\mathrm{a}}(X)$ is called the Néron–Severi group of $X$ and is denoted by $\mathrm{NS}(X)$. The Néron–Severi theorem asserts that th
4 KB (687 words) - 05:47, 15 April 2023
geometry, which reduces the problem of the existence of rational
points on an algebraic variety over a global field to the analogous
3 KB (543 words) - 15:48, 17 February 2012
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...ements points, straight lines, planes, circles, spheres, conics, quadrics, and multi-dimensional analogues of these.
8 KB (1,191 words) - 06:39, 9 April 2023
An [[Algebraic variety|algebraic variety]] which is minimal relative to the existence of birational morphism
...gularities]]) for varieties of arbitrary dimension in characteristic 0 for and for varieties of dimension $n\leq3$ in characteristic $p>5$.
7 KB (1,005 words) - 21:13, 21 November 2018
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of a finite [[CW-complex|CW-complex]] (cf. also [[Cellular space|Cellular space]]) $ X $
11 KB (1,584 words) - 11:51, 8 April 2023
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on a compact [[Complex manifold|complex manifold]] $ X $.
5 KB (719 words) - 22:14, 5 June 2020
[[Cohomology ring|cohomology ring]] of a complex flag manifold $G/P$ (cf. also
[[Linear algebraic group|linear algebraic group]] and $P$ is a
3 KB (371 words) - 18:45, 30 March 2012
...ordinates in a Cartesian coordinate system satisfy an [[Algebraic equation|algebraic equation]] of degree two:
...in the general equation (*), one may transform it by parallel translation and rotation in the coordinate system to one of the 17 canonical forms given be
19 KB (2,446 words) - 17:35, 31 March 2012
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...or finite-dimensional orientable topological manifolds [[#References|[1]]] and for finite cell complexes (see [[#References|[2]]], [[#References|[3]]]). T
10 KB (1,491 words) - 19:04, 26 March 2023