Results 251 to 260 of about 1,240 (281)

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.
Claire Voisin, Voisin Claire
exaly   +2 more sources

On the Hodge conjecture for quasi-smooth intersections in toric varieties [PDF]

open access: yesSao Paulo Journal of Mathematical Sciences, 2021
We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection subvarieties ...
Ugo Bruzzo   +2 more
exaly   +2 more sources

The Hodge conjecture for self-products of certain K3 surfaces

open access: yesJournal of Algebra, 2010
We use a result of van Geemen (2008) [vG4] to determine the endomorphism algebra of the Kuga–Satake variety of a K3 surface with real multiplication.
Schlickewei, Ulrich, Ulrich Schlickewei
exaly   +2 more sources

the Hodge Conjecture

Preprint v1 — A proof of the Hodge conjecture on algebraic cycles and cohomology classes of smooth projective varieties. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings.
openaire   +2 more sources

The Dirac-Dolbeault Operator Approach to the Hodge Conjecture

open access: yesSymmetry
The Dirac-Dolbeault operator for a compact Kähler manifold is a special case of Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows the expression of the values of the sections of the Dirac ...
Simone Farinelli
exaly   +4 more sources

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 ...
openaire   +2 more sources

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