The Hodge conjecture: the complications of understanding the shape of geometric spaces
The Hodge conjecture is one of the seven millennium problems, and is framed within differential geometry and algebraic geometry. It was proposed by William Hodge in 1950 and is currently a stimulus for the development of several theories based on geometry, analysis, and mathematical physics. It prop...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/18768 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/18768 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.12 Complex geometry Topology Homology Hodge theory Manifolds. Geometria algebraica Geometría diferencial Topología 1201.01 Geometría Algebraica 1204.04 Geometría Diferencial 1210 Topología |
| Sumario: | The Hodge conjecture is one of the seven millennium problems, and is framed within differential geometry and algebraic geometry. It was proposed by William Hodge in 1950 and is currently a stimulus for the development of several theories based on geometry, analysis, and mathematical physics. It proposes a natural condition for the existence of complex submanifolds within a complex manifold. Manifolds are the spaces in which geometric objects can be considered. In complex manifolds, the structure of the space is based on complex numbers, instead of the most intuitive structure of geometry, based on real numbers. |
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