Coniveau and the Grothendieck group of varieties

2005/06/10 by Donu Arapura, Arapura, Donu, Su-Jeong Kang +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0506210

Final revision (to appear in Mich. Math. J), 10 pages, latex

arxiv created 2005/11/30 · arxiv updated 2009/12/01

Abstract

It is shown that if the generalized Hodge conjecture, or some weaker form of it, holds for a Calabi-Yau variety then it holds for any Calabi-Yau variety birationally equivalent to it. The key idea is to construct suitable homomorphisms between the Grothendieck group of varieties and the Grothendieck group of the exact category of filtered Hodge structures. This along with motivic integration yields the first statement.

Related

• Functoriality of the coniveau filtration
• Equivalence of Coniveaus
• The integral Hodge conjecture for two-dimensional Calabi-Yau categories
• A note on the Grothendieck group of an abelian variety
• A Survey of the Hodge Conjecture for Abelian Varieties