Coniveau and the Grothendieck group of varieties
Algebraic Geometry
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0506210,
title = {Coniveau and the Grothendieck group of varieties},
author = {Donu Arapura and Su-Jeong Kang},
journal= {arXiv preprint arXiv:math/0506210},
year = {2007}
}
Comments
Final revision (to appear in Mich. Math. J), 10 pages, latex