Coniveau and the Grothendieck group of varieties

Details Coniveau and the Grothendieck group of varieties Coniveau and the Grothendieck group of varieties

2005-06-10

arxiv.org/abs/math/0506210v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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