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

Hodge structures have been generalized for all complex varieties (even if they are singular and non-complete) in the form of mixed Hodge structures,...

In mathematics, mixed Hodge modules are the culmination of Hodge theory, mixed Hodge structures, intersection cohomology, and the decomposition theorem...

of Hodge modules is a generalization. Roughly speaking, a mixed Hodge module on a variety X {\displaystyle X} is a sheaf of mixed Hodge structures over...

particular to an idea of mixed Hodge structure on singular varieties, and to deep analogies with étale cohomology. The Hodge conjecture on the 'middle'...

formula Borel–Moore homology Differential of the first kind Log structure Mixed Hodge structure Residue theorem Poincaré residue Deligne (1970), section II...

the study of deformation theory. In addition, log structures serve to define the mixed Hodge structure on any smooth complex variety X, by taking a compactification...

(for varieties over C {\displaystyle \mathbb {C} } ) comes with a mixed Hodge structure, it is a differential-geometric invariant l-adic cohomology (over...

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

Mixed Hodge Structures, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer Verlag 2008 with Steven Zucker: Variation of mixed Hodge structure...

Hodge conjecture, for some applications. The theory of mixed Hodge structures, a powerful tool in algebraic geometry that generalizes classical Hodge...

Singular solution Stratification (mathematics) Intersection homology Mixed Hodge structure Whitney umbrella Round function Victor Goryunov Arnold, V. I. (2000)...

this construction gives the trefoil knot its structure as a fibered knot. Vanishing cycle Mixed Hodge structure Dimca, Alexandru (1992). Singularities and...

Topologically stratified space Intersection theory Perverse sheaf Mixed Hodge structure Warning: there is more than one convention for the way that the...

org/abs/math/0203273. Peters, Chris A. M.; Steenbrink, Joseph H. M. Mixed Hodge structures. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series...

some applications, such as the construction of Pierre Deligne's mixed Hodge structures. Many other coherent sheaf cohomology groups are found using an...

spectral sequence. Hodge–de Rham spectral sequence Spectral sequence of a double complex Can be used to construct Mixed Hodge structures Another common spectral...

resolution Gerbe Peters, Chris A.M.; Steenbrink, Joseph H.M. (2008). Mixed Hodge Structures. Springer Berlin, Heidelberg. ISBN 978-3-540-77017-6. Cartan, H...

University (Paris VI) with thesis advisor Daniel Bertrand and thesis Structure de Hodge, équations différentielles p-adiques, et indépendance algébrique de...

1090/S0273-0979-07-01178-0. MR 2338364. Kulikov, Valentine (1998), Mixed Hodge Structures and Singularities, Cambridge Tracts in Mathematics, pp. 1–59 (Gives...

trace methods. Malcev Lie algebras also arise in the theory of mixed Hodge structures. Goodwillie, Thomas G. (1986), "Relative algebraic K-theory and...

can be genetically traced to having mixed Polynesian/Melanesian ancestry. The Indo-Fijian population is also a hodge-podge of South Asian immigrants (called...

Schechtman, V. V.; Varchenko, A. N. (1990). "Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane". Grothendieck...

smooth complex algebraic varieties, using Deligne's formulation of mixed Hodge structures to extend the Kähler decomposition of smooth differential forms...

Ann. 345 (2009), 453–489. C. Florentino, S. Lawton and J. Silva Mixed Hodge structures on character varieties of nilpotent groups, Rev. Mat. Complutense...

perverse sheaves, and the theory of variation of Hodge structures and mixed Hodge structures (introduced by Pierre Deligne) in algebraic geometry. This...

point of a vector field, the Petrovskiĭ-Oleĭnik inequalities, and mixed Hodge structures". Functional Analysis and Its Applications. 12 (1): 1–12. doi:10...

elements in Hodge's music are the incorporation of timbre as an integral form-bearing compositional device and an approach to musical structure that emphasizes...

Mark Levine observes that when mixed in with more conventional "playing the changes", pentatonic scales provide "structure and a feeling of increased space"...

A mixed-signal integrated circuit is any integrated circuit that has both analog circuits and digital circuits on a single semiconductor die. Their usage...