Search: MSC category 14C30
( Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture )
1. CMB Online first
||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
2. CMB Online first
||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
3. CMB 2007 (vol 50 pp. 161)
||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.
4. CMB 2004 (vol 47 pp. 566)
||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.