Results 221 to 230 of about 26,779 (258)

The Hodge Conjecture

2016
This is an introduction to the Hodge conjecture, which, although intended to a general mathematical audience, assumes some knowledge of topology and complex geometry. The emphasis will be put on the importance of the notion of Hodge structure in complex algebraic geometry.
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Hodge Conjecture Mathematical Proof

This paper presents a comprehensive and formal proof of the Hodge Conjecture, a foundational problem in algebraic geometry proposed by W.V.D. Hodge in 1950. The conjecture asserts that for any smooth projective variety  X , every rational (1,1)-Hodge class can be represented by an algebraic cycle.
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ABELIAN VARIETIES AND THE GENERAL HODGE CONJECTURE

Russian Academy of Sciences. Izvestiya Mathematics, 1994
This paper discusses the generalized Hodge-Grothendieck conjecture in the case of abelian varieties. This conjecture asserts that if \(X\) is a smooth \(n\)-dimensional projective variety over \(\mathbb{C}\) then \(F^r_c H^i(X,\mathbb{Q})\) is the largest Hodge \(\mathbb{Q}\)-substructure contained in \(H^i(X, \mathbb{Q}) \cap F^rH^i (X,\mathbb{Q ...
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Hodge Conjecture – Structural Resolution

Using fold-based representation of Φ functors and cotangent bundles, this work provides a symbolic structural pathway to resolving the Hodge Conjecture. Residue-cycle decomposition and projective flow are expressed as fold-mappable structures under slot coherence constraints.
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Proof of Hodge's conjecture

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Hodge and generalized Hodge conjectures, coniveau and algebraic cycles

Journal of Open Mathematical Problems
This is a survey of the Hodge conjecture, with emphasis on its companion, the generalized Hodge conjecture, which involves the theory of Hodge structures, algebraic cycles and motives.
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THE HODGE CONJECTURE

2022
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SOLUTION OF THE HODGE CONJECTURE

Sir William Vallance Douglas Hodge (1903-1975) proposed the famousHodge Conjecture, one of the most important and complex problems inmodern mathematics concerning the structure of certain geometric spaces,which connects algebraic geometry with differential geometry.
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On the Hodge conjecture for quasi-smooth intersections in toric varieties

Sao Paulo Journal of Mathematical Sciences, 2021
Ugo Bruzzo, William Montoya
exaly  

A Solution to the Hodge Conjecture

This work proposes a variational approach to the Hodge Conjecture for smooth, projective complex Kähler manifolds. The author introduces a geometrically motivated functional Ω[α], defined on the space of harmonic representatives of rational Hodge classes α ∈ H²ᵖ(X,ℚ) ∩ Hᵖ,ᵖ(X).
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