to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge. For example, in an oriented 3-dimensional...

reading de Rham's thesis, Hodge realized that the real and imaginary parts of a holomorphic 1-form on a Riemann surface were in some sense dual to each...

mathematician William Vallance Douglas Hodge as a result of a work in between 1930 and 1940 to enrich the description of de Rham cohomology to include extra...

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...

Sir William Vallance Douglas Hodge FRS FRSE (/hɒdʒ/; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer. His discovery of...

other lies the de Rham cohomology. The de Rham cohomology has inspired many mathematical ideas, including Dolbeault cohomology, Hodge theory, and the...

complex algebraic varieties. In this setting, the Serre duality theorem is an application of Hodge theory for Dolbeault cohomology, and may be seen as a...

involution operation: if the dual of A is B, then the dual of B is A. In other cases the dual of the dual – the double dual or bidual – is not necessarily...

Retrieved 2017-03-06. Nicolaescu, Liviu. "Hodge Numbers of Complete Intersections" (PDF). Candelas, Philip; de la Ossa, Xenia C.; Green, Paul S.; Parkes...

the anti-self-duality equations. When the dimension of the base manifold X {\displaystyle X} is four, a coincidence occurs: the Hodge star operator maps...

diamond Hodge duality Hodge filtration Hodge index theorem Hodge group Hodge star operator Hodge structure Mixed Hodge structure Hodge–Tate module Hodge theory...

lattices Dualizing complex Dualizing sheaf Eckmann–Hilton duality Esakia duality Fenchel's duality theorem Hodge dual Isbell duality Jónsson–Tarski duality Lagrange...

In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It...

A dual-purpose gun is a naval artillery mounting designed to engage both surface and air targets. Second World War-era capital ships had four classes of...

from Serre duality. A simple consequence of Hodge theory is that every odd Betti number b2a+1 of a compact Kähler manifold is even, by Hodge symmetry....

making it a toy model for quantum gravity. The Killing form involves the Hodge dual. Witten later changed his mind, and argued that nonperturbatively 2+1D...

In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and...

10003B. Batyrev, Victor V.; Borisov, Lev A. (1996). "Mirror duality and string theoretic Hodge numbers". Inventiones Mathematicae. 126 (1): 183–203. arXiv:alg-geom/9509009...

commentary by Buddhaguhya was written in about 760 and is preserved in Tibetan. Hodge translates it into English alongside the text itself. Four originally Sanskrit...

Infantry Division in South Korea. Hodges served as a battalion executive officer with the 101st Airborne before becoming aide-de-camp to the Supreme Allied Commander...

ISBN 3540051902, MR 0417174, OCLC 169357 Deligne, Pierre (1971), "Théorie de Hodge II", Publ. Math. IHÉS, 40: 5–57, doi:10.1007/BF02684692, MR 0498551, S2CID 118967613...

"David Taylor Wins Hodge Trophy Award for Second Time". Penn State Athletics. 2014-04-01. Retrieved 2024-04-04. "Penn State wrestling: Dual meet win streak...

surface Del Pezzo surface Rational surface Enriques surface K3 surface Hodge index theorem Elliptic surface Surface of general type Zariski surface Algebraic...

Hodge star additionally needs a choice of orientation, and produces the Hodge dual of its argument. Given a local bundle chart, the covariant derivative...

the conformal structure on the Riemann surface intrinsically defines a Hodge star operator on 1-forms (or differentials) without specifying a Riemannian...

physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric-magnetic duality, as an S-duality, predicted...

Kingsmere Anon. (S. G. Shaw) Detective Library 42 Kingsmere College: Educating Hodge Anon. (S. G. Shaw) Detective Library 43 Kingsmere College: The End of the...

pseudo-Riemannian manifold, k-forms correspond to k-vector fields (by duality via the metric), so there is a notion of a vector field corresponding to...

the second spectral sequence from above gives the Hodge-de Rham spectral sequence for algebraic de Rham cohomology: E 1 p , q = H q ( X , Ω X p ) ⇒ H...

Theatrical Flag in U.S. (EXCLUSIVE)". Variety. Retrieved October 1, 2024. Hodges, Jake (October 1, 2024). "'The Substance' is Already MUBI's Biggest Domestic...