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Search: MSC category 14C30 ( Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture )

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1. CMB Online first

Wang, Zhenjian
On Deformations of Nodal Hypersurfaces
We extend the infinitesimal Torelli theorem for smooth hypersurfaces to nodal hypersurfaces.

Keywords:nodal hypersurface, deformation, Torelli theorem
Categories:32S35, 14C30, 14D07, 32S25

2. CMB 2015 (vol 59 pp. 144)

Laterveer, Robert
A Brief Note Concerning Hard Lefschetz for Chow Groups
We formulate a conjectural hard Lefschetz property for Chow groups, and prove this in some special cases: roughly speaking, for varieties with finite-dimensional motive, and for varieties whose self-product has vanishing middle-dimensional Griffiths group. An appendix includes related statements that follow from results of Vial.

Keywords:algebraic cycles, Chow groups, finite-dimensional motives
Categories:14C15, 14C25, 14C30

3. CMB 2015 (vol 58 pp. 519)

Kang, Su-Jeong
Refined Motivic Dimension
We define a refined motivic dimension for an algebraic variety by modifying the definition of motivic dimension by Arapura. We apply this to check and recheck the generalized Hodge conjecture for certain varieties, such as uniruled, rationally connected varieties and a rational surface fibration.

Keywords:motivic dimension, generalized Hodge conjecture
Categories:14C30, 14C25

4. CMB 2007 (vol 50 pp. 161)

Arapura, Donu; Kang, Su-Jeong
Functoriality of the Coniveau Filtration
It is shown that the coniveau filtration on the cohomology of smooth projective varieties is preserved up to shift by pushforwards, pullbacks and products.


5. CMB 2004 (vol 47 pp. 566)

Koike, Kenji
Algebraicity of some Weil Hodge Classes
We show that the Prym map for 4-th cyclic \'etale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.


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