Aviso: para depositar documentos, por favor, inicia sesión e identifícate con tu cuenta de correo institucional de la UCM con el botón MI CUENTA UCM. No emplees la opción AUTENTICACIÓN CON CONTRASEÑA
 

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

Simple item page
dc.contributor.authorMuñoz, Vicente
dc.date.accessioned2023-06-17T22:41:49Z
dc.date.available2023-06-17T22:41:49Z
dc.date.issued2018
dc.description.abstractThe 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.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/55156
dc.identifier.doi10.7203/metode.8.8253
dc.identifier.issn2174-9221
dc.identifier.officialurlhttps://ojs.uv.es/index.php/Metode/article/view/8253/11889
dc.identifier.relatedurlhttps://ojs.uv.es/index.php/Metode/index
dc.identifier.urihttps://hdl.handle.net/20.500.14352/18768
dc.issue.number8
dc.journal.titleMètode Science Studies Journal - Annual Review
dc.language.isoeng
dc.page.final57
dc.page.initial51
dc.publisherUniversitat de València
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.cdu515.12
dc.subject.keywordComplex geometry
dc.subject.keywordTopology
dc.subject.keywordHomology
dc.subject.keywordHodge theory
dc.subject.keywordManifolds.
dc.subject.ucmGeometria algebraica
dc.subject.ucmGeometría diferencial
dc.subject.ucmTopología
dc.subject.unesco1201.01 Geometría Algebraica
dc.subject.unesco1204.04 Geometría Diferencial
dc.subject.unesco1210 Topología
dc.titleThe Hodge conjecture: the complications of understanding the shape of geometric spaces
dc.typejournal article
dcterms.referencesAtiyah, M. F., & Hirzebruch, F. (1962). Analytic cycles on complex manifolds. Topology, 1, 25–45. doi: 10.1016/0040-9383(62)90094-0 Grothendieck, A. (1969). Hodge’s general conjecture is false for trivial reasons. Topology, 8, 299–303. doi: 10.1016/0040-9383(69)90016-0 Hodge, W. V. D. (1950). The topological invariants of algebraic varieties. In Proceedings of the International Congress of Mathematicians (pp. 181– 192). Cambridge, MA: American Mathematical Society. Poincaré, H. (1895). Analysis situs. Journal de l’École Polytechnique, 1, 1–123. Voisin, C. (2002). A counterexample to the Hodge Conjecture extended to Kähler varieties. International Mathematics Research Notices, 20, 1057–1075. doi: 10.1155/S1073792802111135 Weil, A. (1980). Abelian varieties and the Hodge ring. In Oeuvres Scientifiques Collected Papers III (pp. 421–429). New York: Springer-Verlag.
dspace.entity.typePublication

Download

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
VMuñoz110.pdf
Size:
791.23 KB
Format:
Adobe Portable Document Format
downoload Download

Collections

Artículos