- Hodge theorem
Hodge theorem may refer to:
*
Hodge theory
*Hodge index theorem
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Hodge theorem
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Hodge theory — In mathematics, Hodge theory is one aspect of the study of the algebraic topology of a smooth manifold M . More specifically, it works out the consequences for the cohomology groups of M , with real coefficients, of the partial differential… … Wikipedia
Hodge dual — In mathematics, the Hodge star operator or Hodge dual is a significant linear map introduced in general by W. V. D. Hodge. It is defined on the exterior algebra of a finite dimensional oriented inner product space. Contents 1 Dimensions and… … Wikipedia
Hodge conjecture — The Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de… … Wikipedia
Hodge structure — In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. A mixed Hodge… … Wikipedia
Hodge index theorem — In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V . It says, roughly speaking, that the space spanned by such curves (up to linear equivalence)… … Wikipedia
Hodge cycle — In mathematics, a Hodge cycle is a particular kind of homology class defined on a complex algebraic variety V , or more generally on a Kähler manifold. A homology class x in a homology group : H k ( V , C ) = H where V is a non singular complex… … Wikipedia
William Hodge — William Vallance Douglas Hodge (* 17. Juni 1903 in Edinburgh; † 7. Juli 1975 in Cambridge) war ein britischer Mathematiker. Leben und Wirken Er war der Sohn von Janet Vallence, Tochter eines Süßwarenhändlers, und Archibald James Hodge, einem… … Deutsch Wikipedia
William Vallance Douglas Hodge — (* 17. Juni 1903 in Edinburgh; † 7. Juli 1975 in Cambridge) war ein britischer Mathematiker. Inhaltsverzeichnis 1 Leben und Wirken 2 Werke 3 Literatur … Deutsch Wikipedia
W. V. D. Hodge — William Vallance Douglas Hodge FRS (17 June 1903 7 July 1975) was a Scottish mathematician, specifically a geometer. His discovery of far reaching topological relations between algebraic geometry and differential geometry mdash; an area now… … Wikipedia
Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) … Wikipedia
