On K_1 and K_2 of algebraic surfaces

Details On K_1 and K_2 of algebraic surfaces On K_1 and K_2 of algebraic surfaces

2002-02-18

arxiv.org/abs/math/0202173v1

Mathematics

Algebraic Geometry

23 pages, amstex. Appendix by Alberto Collino (Torino)

Scientific paper

We study the higher Chow groups $CH^2(X,1)$ and $CH^3(X,2)$ of smooth, projective algebraic surfaces over a field of char 0. We develop a theoretical framework to study them by using so-called higher normal functions and higher infinitesimal invariants when the cycles are supported on normal crossing divisors. Then we investigate their structure on hypersurfaces in projective 3-space. This leads to vanishing or decomposbility results. On the other hand we find examples of these groups in degrees 4 and 5 where the result is a highly indecomposably (hence big) abelian group. Part of the examples are due to Alberto Collino.

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