#REDIRECT [[K3-surface]]
24 bytes (3 words) - 13:58, 11 July 2018
...kind of [[K3-surface|$K3$-surface]]; it is determined within the class of $K3$-surfaces by the condition that it contains 16 irreducible rational curves.
A quartic surface in $P^3$ has at most 16 double points (as has the Kummer surface).
2 KB (248 words) - 12:27, 12 November 2023
$#C+1 = 72 : ~/encyclopedia/old_files/data/K055/K.0505040 \BMI K3\EMI\AAhsurface
A smooth projective [[Algebraic surface|algebraic surface]] $ X $
10 KB (1,443 words) - 15:43, 1 March 2022
...cture of a hyper-Kähler manifold. A K3-surface (cf. [[Surface, K3|Surface, K3]]) is a compact hyper-Kähler manifold.
...otient singularities obtained from a minimal [[Algebraic surface|algebraic surface]] of general type by blowing down $( - 2 )$-curves has the structure of a K
4 KB (662 words) - 19:35, 7 February 2024
...elliptic curve|hyper-elliptic curve]]. A non-singular algebraic projective surface $ X $
...ssumed to hold), any double plane is birationally isomorphic to the affine surface given in three-dimensional affine space by an equation
5 KB (749 words) - 07:33, 22 December 2023
...ion of the global Torelli problem (1984) is the case of a [[K3-surface| $ K3 $-
...]. The Torelli theorem has also been generalized to the case of Kähler $ K3 $-
6 KB (967 words) - 08:26, 6 June 2020
$#C+1 = 58 : ~/encyclopedia/old_files/data/A012/A.0102450 Analytic surface (in algebraic geometry)
...analogous to that of algebraic surfaces (cf. [[Algebraic surface|Algebraic surface]]) — a fact which largely reduces the theory of analytic surfaces to that
8 KB (1,169 words) - 18:47, 5 April 2020
of the canonical class gives a birational mapping of the surface onto its image in projective space. They are called surfaces of general typ
...rojective space which is a birational mapping. For example, a non-singular surface of degree $ m $
5 KB (747 words) - 06:29, 30 May 2020
...ed, an algebraic surface will be understood to mean a projective algebraic surface over an algebraically closed field $ k $.
...|[9]]]. The proof of the existence of a non-singular model of an algebraic surface for the case of a ground field with positive characteristic was given in 19
26 KB (3,736 words) - 13:08, 8 February 2020
...image of a period mapping generally relate to the cases of curves and $ K3 $-
surfaces (cf. [[K3-surface| $ K3 $-
12 KB (1,699 words) - 09:49, 20 December 2019
$#C+1 = 180 : ~/encyclopedia/old_files/data/E035/E.0305550 Elliptic surface
An algebraic or analytic complete non-singular surface $ X $
15 KB (2,046 words) - 05:46, 13 June 2022
...are exhausted by the complex $ K3 $-surfaces (cf. [[K3-surface| $ K3 $-surface]]).
14 KB (2,063 words) - 02:45, 18 July 2022
...Katz [[#References|[Ka]]] used an existence result of Mori's for curves on K3 surfaces to extend Clemens' argument to '''every''' positive value of <math
...lse for double covers of <math>\mathbb{P}^3</math> ramified along an octic surface''. Indeed, the preimages in the double cover of lines that intersect the oc
14 KB (2,200 words) - 18:27, 23 October 2017
...compact manifolds of complex dimension 2 (cf. [[Analytic surface|Analytic surface]]).
is a compact Riemann surface and
41 KB (5,916 words) - 11:24, 26 March 2023