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The Hodge conjecture: the complications of understanding the shape of geometric spaces

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Muñoz, Vicente (2018) The Hodge conjecture: the complications of understanding the shape of geometric spaces. Mètode Science Studies Journal - Annual Review (8). pp. 51-57. ISSN 2174-9221

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Official URL: https://ojs.uv.es/index.php/Metode/article/view/8253/11889




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Complex geometry, Topology, Homology, Hodge theory, Manifolds.
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Topology
ID Code:55156
Deposited On:30 Apr 2019 17:28
Last Modified:30 Apr 2019 17:28

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