| http://dbpedia.org/ontology/abstract
|
In mathematics, mirror symmetry is a conje … In mathematics, mirror symmetry is a conjectural relationship between certain Calabi–Yau manifolds and a constructed "mirror manifold". The conjecture allows one to relate the number of rational curves on a Calabi-Yau manifold (encoded as Gromov–Witten invariants) to integrals from a family of varieties (encoded as period integrals on a variation of Hodge structures). In short, this means there is a relation between the number of genus algebraic curves of degree on a Calabi-Yau variety and integrals on a dual variety . These relations were original discovered by Candelas, De la Ossa, Green, and Parkes in a paper studying a generic quintic threefold in as the variety and a construction from the quintic Dwork family giving . Shortly after, Sheldon Katz wrote a summary paper outlining part of their construction and conjectures what the rigorous mathematical interpretation could be.rous mathematical interpretation could be.
, 거울 대칭 가설은 특정 칼라비-야우 다양체와 그 다양체의 "거울 다양체"사이의 관계에 대한 추측이다. 이 추측으로 칼라비-야우 다양체 상의 유리 곡선의 수를 대수다양체 족에서 적분과 관련시킬 수 있다. 거울 대칭 가설을 다루는 몇 가지 관점이 있으며, 대표적으로 호몰로지 거울 대칭 가설과 SYZ 가설이 있다. 호몰로지 거울 대칭 가설은 호몰로지 대수학을 기반으로 삼는 반면, SYZ 추측은 더욱 기하학적인 서술이다.
|
| http://dbpedia.org/ontology/wikiPageExternalLink
|
http://www.claymath.org/library/monographs/cmim01c.pdf +
, https://bookstore.ams.org/surv-68-s +
, https://ocw.mit.edu/courses/mathematics/18-969-topics-in-geometry-mirror-symmetry-spring-2009/lecture-notes/ +
|
| http://dbpedia.org/ontology/wikiPageID
|
64540037
|
| http://dbpedia.org/ontology/wikiPageLength
|
23141
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1096463237
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Dwork_family +
, http://dbpedia.org/resource/Clay_Mathematics_Institute +
, http://dbpedia.org/resource/Deformation_%28mathematics%29 +
, http://dbpedia.org/resource/Correlation_function_%28quantum_field_theory%29 +
, http://dbpedia.org/resource/Euler_characteristic +
, http://dbpedia.org/resource/Category:Mathematical_physics +
, http://dbpedia.org/resource/Electromagnetism +
, http://dbpedia.org/resource/Supersymmetry +
, http://dbpedia.org/resource/Quantum_state +
, http://dbpedia.org/resource/Singularity_%28mathematics%29 +
, http://dbpedia.org/resource/Homotopy_associative_algebra +
, http://dbpedia.org/resource/Quintic_threefold +
, http://dbpedia.org/resource/Weak_Force +
, http://dbpedia.org/resource/Euler_class +
, http://dbpedia.org/resource/Moduli_space +
, http://dbpedia.org/resource/Heterotic_string_theory +
, http://dbpedia.org/resource/Algebraic_curve +
, http://dbpedia.org/resource/Homogeneous_polynomial +
, http://dbpedia.org/resource/Pseudoholomorphic_curve +
, http://dbpedia.org/resource/Kuranishi_structure +
, http://dbpedia.org/resource/Kodaira%E2%80%93Spencer_map +
, http://dbpedia.org/resource/Complexified +
, http://dbpedia.org/resource/Proj_construction +
, http://dbpedia.org/resource/Moduli_of_algebraic_curves +
, http://dbpedia.org/resource/Calabi%E2%80%93Yau_manifold +
, http://dbpedia.org/resource/Newlander%E2%80%93Nirenberg_theorem +
, http://dbpedia.org/resource/Mirror_symmetry_%28string_theory%29 +
, http://dbpedia.org/resource/Period_%28algebraic_geometry%29 +
, http://dbpedia.org/resource/Yukawa_coupling +
, http://dbpedia.org/resource/Chern_class +
, http://dbpedia.org/resource/Symplectic_geometry +
, http://dbpedia.org/resource/Gromov%E2%80%93Witten_invariant +
, http://dbpedia.org/resource/Lefschetz_hyperplane_theorem +
, http://dbpedia.org/resource/Line_bundle +
, http://dbpedia.org/resource/Virtual_fundamental_class +
, http://dbpedia.org/resource/Rational_curve +
, http://dbpedia.org/resource/Canonical_bundle +
, http://dbpedia.org/resource/Vector_bundle +
, http://dbpedia.org/resource/Category:Algebraic_geometry +
, http://dbpedia.org/resource/Arxiv:1609.00624 +
, http://dbpedia.org/resource/Serre_duality +
, http://dbpedia.org/resource/Arxiv:1705.06667 +
, http://dbpedia.org/resource/Arxiv:1501.00730 +
, http://dbpedia.org/resource/Cotangent_complex +
, http://dbpedia.org/resource/Arxiv:1510.03839 +
, http://dbpedia.org/resource/Arxiv:1103.4956 +
, http://dbpedia.org/resource/Algebraic_torus +
, http://dbpedia.org/resource/Arxiv:1111.0632 +
, http://dbpedia.org/resource/ArXiv:math/9805097v2 +
, http://dbpedia.org/resource/Arxiv:0812.1171 +
, http://dbpedia.org/resource/Generation_%28particle_physics%29 +
, http://dbpedia.org/resource/Category:String_theory +
, http://dbpedia.org/resource/Arxiv:math/9812003 +
, http://dbpedia.org/resource/Bogomolev-Tian-Todorov_theorem +
, http://dbpedia.org/resource/Arxiv:math/9806133 +
, http://dbpedia.org/resource/Arxiv:math/9807070 +
, http://dbpedia.org/resource/Calabi-Yau +
, http://dbpedia.org/resource/Arxiv:alg-geom/9712011 +
, http://dbpedia.org/resource/Arxiv:math/9801119 +
, http://dbpedia.org/resource/Arxiv:alg-geom/9310003 +
, http://dbpedia.org/resource/Variation_of_Hodge_structure +
, http://dbpedia.org/resource/Arxiv:1111.4234 +
, http://dbpedia.org/resource/Arxiv:alg-geom/9603021 +
, http://dbpedia.org/resource/Category:Conjectures +
, http://dbpedia.org/resource/Variation_of_Hodge_structures +
, http://dbpedia.org/resource/Non-linear_sigma_model +
, http://dbpedia.org/resource/Automorphism_group +
, http://dbpedia.org/resource/Conformal_equivalence +
, http://dbpedia.org/resource/K%C3%A4hler_manifold +
, http://dbpedia.org/resource/Almost-complex_structure +
, http://dbpedia.org/resource/Kontsevich_moduli_space +
, http://dbpedia.org/resource/Interior_product +
, http://dbpedia.org/resource/String_theory +
, http://dbpedia.org/resource/Feynman_path_integral +
, http://dbpedia.org/resource/Sheldon_Katz +
, http://dbpedia.org/resource/Hodge_structure +
, http://dbpedia.org/resource/Hilbert_space +
, http://dbpedia.org/resource/Poincar%C3%A9_duality +
, http://dbpedia.org/resource/Blowing_up +
, http://dbpedia.org/resource/Geometric_invariant_theory +
, http://dbpedia.org/resource/Crepant_resolution +
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Rp +
, http://dbpedia.org/resource/Template:See_also +
, http://dbpedia.org/resource/Template:Other_uses +
, http://dbpedia.org/resource/Template:Technical +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Algebraic_geometry +
, http://dbpedia.org/resource/Category:Mathematical_physics +
, http://dbpedia.org/resource/Category:Conjectures +
, http://dbpedia.org/resource/Category:String_theory +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Mirror_symmetry_conjecture?oldid=1096463237&ns=0 +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Mirror_symmetry_conjecture +
|
| owl:sameAs |
http://ko.dbpedia.org/resource/%EA%B1%B0%EC%9A%B8_%EB%8C%80%EC%B9%AD_%EA%B0%80%EC%84%A4 +
, http://www.wikidata.org/entity/Q97366912 +
, https://global.dbpedia.org/id/D1jB7 +
, http://dbpedia.org/resource/Mirror_symmetry_conjecture +
|
| rdfs:comment |
거울 대칭 가설은 특정 칼라비-야우 다양체와 그 다양체의 "거울 다양체"사이의 관계에 대한 추측이다. 이 추측으로 칼라비-야우 다양체 상의 유리 곡선의 수를 대수다양체 족에서 적분과 관련시킬 수 있다. 거울 대칭 가설을 다루는 몇 가지 관점이 있으며, 대표적으로 호몰로지 거울 대칭 가설과 SYZ 가설이 있다. 호몰로지 거울 대칭 가설은 호몰로지 대수학을 기반으로 삼는 반면, SYZ 추측은 더욱 기하학적인 서술이다.
, In mathematics, mirror symmetry is a conje … In mathematics, mirror symmetry is a conjectural relationship between certain Calabi–Yau manifolds and a constructed "mirror manifold". The conjecture allows one to relate the number of rational curves on a Calabi-Yau manifold (encoded as Gromov–Witten invariants) to integrals from a family of varieties (encoded as period integrals on a variation of Hodge structures). In short, this means there is a relation between the number of genus algebraic curves of degree on a Calabi-Yau variety and integrals on a dual variety . These relations were original discovered by Candelas, De la Ossa, Green, and Parkes in a paper studying a generic quintic threefold in as the variety and a construction from the quintic Dwork family giving . Shortly after, Sheldon Katz wrote a summary paper outlining pdon Katz wrote a summary paper outlining p
|
| rdfs:label |
Mirror symmetry conjecture
, 거울 대칭 가설
|
| rdfs:seeAlso |
http://dbpedia.org/resource/Mirror_symmetry_%28string_theory%29 +
|
