%0 Journal Article %T Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections %A Lie Fu %J Mathematics %D 2012 %I arXiv %X On one hand, for a general Calabi-Yau complete intersection X, we establish a decomposition, up to rational equivalence, of the small diagonal in X^3, from which we deduce that any decomposable 0-cycle of degree 0 is in fact rationally equivalent to 0, up to torsion. On the other hand, we find a similar decomposition of the smallest diagonal in a higher power of a hypersurface, which provides us an analogous result on the multiplicative structure of its Chow ring. %U http://arxiv.org/abs/1209.5616v1