Algebraic cycles and Todorov surfaces

摘要

Motivated by the Bloch-Beilinson conjectures, Voisin has formulated a conjecture about 0-cycles on self-products of surfaces of geometric genus one. We verify Voisin's conjecture for the family of Todorov surfaces with K-2 = 2 and fundamental group Z/2Z. As a by-product, we prove that certain Todorov surfaces have finite-dimensional motive.