Algebraic cycles and Todorov surfaces

Abstract

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 $\mathbb{Z}/2\mathbb{Z}$. As a by-product, we prove that certain Todorov surfaces have finite-dimensional motive.

arXiv commentTo appear in Kyoto Journal of Mathematics, 31 pages, comments still welcome !

References in corpus (3)

• The motive of a classifying space
• Symplectic involutions of K3 surfaces act trivially on CH_0
• The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II

Cited by in corpus (8)

• On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
• Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type
• Algebraic cycles on Todorov surfaces of type $(2,12)$
• Zero-cycles on self-products of varieties: some elementary examples verifying Voisin's conjecture
• Bloch's conjecture for some numerical Campedelli surfaces
• Zero-cycles on Garbagnati surfaces
• On the Chow ring of some special Calabi-Yau varieties
• Zero-cycles on Cancian-Frapporti surfaces