We focus on Voisin's conjecture on 0-cycles on the self-product of surfaces of geometric genus one, which arises in the context of the Bloch-Beilinson filtration conjecture. We verify this conjecture for the family of Todorov surfaces of type (2, 12), giving an explicit description of this family as quotient surfaces of the complete intersection of four quadrics in P 6 . We give some motivic applications.
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