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K3 surface

Dans la seconde partie de mon rapport, il s'agit des variétés kählériennes dites K3, ainsi nommées en l'honneur de Kummer, Kähler, Kodaira et de la belle montagne K2 au Cachemire. In the second part of my report, we deal with the Kähler varieties known as K3, named in honor of Kummer, Kähler, Kodaira and of the beautiful mountain K2 in Kashmir.

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Overview

Definition

Calculation of the Betti numbers

Properties

Examples

The Picard lattice

Elliptic K3 surfaces

Rational curves on K3 surfaces

The period map

Moduli spaces of projective K3 surfaces

The ample cone and the cone of curves

Automorphism group

Relation to string duality

History

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K3 surface

Nodes149
Edges148
Triples287
Avg. degree1.99
Density0.013423
Components1

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K3 surface

Top relations

related to References · 113
K3 surface → Adv, Advanced Mathematics, AF, Alexandru, American Mathematical Society, André, Annales Scientifiques, Antonius, Arnaud, Aspinwall, Astérisque, Atti, Berlin, Bibcode, Bologna, Boulder, Bourbaki, Bourguignon, Cambridge Studies, Cambridge University Press
related to Properties · 32
K3 surface → Alexey Rudakov, Analogously, Any, Betti, By Shing-Tung Yau's, Calabi, E8, Every, For, For K3, Hodge, Igor Shafarevich, II, In, Jacobian, John Morgan, K3, Kodaira, Kunihiko Kodaira, Kähler
related to history · 19
K3 surface → An, André Weil, Arthur Cayley, Daniel Burns, Enriques, Ernst Kummer, Federigo Enriques, Francesco Severi, Friedrich Schur, He, Igor Shafarevich, Ilya Piatetski-Shapiro, In, K3, Kunihiko Kodaira, Michael Rapoport, More, Quartic, Torelli
related to Elliptic K3 surfaces · 14
K3 surface → An, Elliptic, Euler, In, It, K3, Kodaira, Namely, Pic, Picard, So, The, There, Whether
related to Relation to string duality · 12
K3 surface → Aspinwall, E8, For, IIA, IIB, K3, M-theory, Spin, String, The, Type IIA, Z2
related to The ample cone and the cone of curves · 12
K3 surface → By, Call, Case, Hodge, It, K3, Pic, Picard, The, Then, There, Thus
related to Automorphism group · 11
K3 surface → Aut, By, Delta, Hans Sterk, K3, Namely, Pic, Picard, Then, Torelli, Weyl
related to The Picard lattice · 11
K3 surface → By, For, In, It, Jean-Pierre Serre's GAGA, K3, Over, Pic, Picard, The, The Picard
related to Rational curves on K3 surfaces · 10
K3 surface → Another, David Mumford, Fedor Bogomolov, In, K3, Kobayashi, On, Pezzo, The, These
related to Examples · 9
K3 surface → Jacobian, K3, Kummer, More, Picard, The, This, Val, When

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Important terminology

k3 surfaces displaystyle surface complex algebraic analytic moduli dimension picard curves genus projective lattice smooth cone group mr pic space

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
K3 surfaceis acompact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity zero0.90text
K3 surfaceis aK3 surface0.90text
K3 surfaceis aabelian group Pic0.90text
del Pezzo surfacesinstance ofRational curves on K3 surfacesIn contrast to positively curved varieties0.80text
a complex algebraic K3 surface X is not uniruledinstance ofRational curves on K3 surfacesIn contrast to positively curved varieties0.80text
surfaces of general typeinstance ofin contrast to negatively curved varieties0.80text
X contains a large discrete set of rational curvesinstance ofin contrast to negatively curved varieties0.80text
K3 surfacerelated to Automorphism groupK30.60section
K3 surfacerelated to Automorphism groupBy0.60section
K3 surfacerelated to Automorphism groupTorelli0.60section
K3 surfacerelated to Automorphism groupPicard0.60section
K3 surfacerelated to Automorphism groupNamely0.60section

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