1. 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
2. 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.
3. 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.