Zero-cycles on Calabi-Yau three-folds with algebraic fiber space structure
Since the work of Beauville and Voisin on Chow rings of K3 surfaces, the intersection theory for varieties with trivial canonical bundle reveals some special properties. More precisely for Calabi-Yau n-folds, one asks the existence of the so-called canonical zero-cycle, an element in CH0 such that any intersection product of n divisor classes is proportional to it. I would like to report a joint work in progress with Hsueh-Yung Lin, which gives new evidence for this property. The variety considered in our work is Calabi-Yau 3-folds with an algebraic fiber space structure. The structural result of Oguiso is important to our approach.