Zero-cycles on self-products of surfaces: some new examples verifying Voisin’s conjecture

Zero-cycles on self-products of varieties: some elementary examples verifying Voisin's conjecture

“…(of Corollary 1.3.) As Voisin had already remarked [28, Corollary 3.5.1], this is implied by the truth of Conjecture 1.1 for X (the implication can be seen using the Bloch-Srinivas argument [4]; this is explained in detail in [18,Corollary 2.7]).…”

“…Examples of surfaces of geometric genus 1 verifying the conjecture (or a variant conjecture) are given in [28], [12], [14], [15], [30]. Examples of other varieties verifying the conjecture are given in [28], [18], [13], [16], [17], [19], [2], [20], [27], [5].…”

Algebraic cycles on Todorov surfaces of type $(2,12)$

“…There are few examples in which Conjecture 1 has been verified (see [Voi96], [Lat16c], [Lat18b], [Lat16a]), but it is still open for a general K3 surface. There are some examples in which a generalization of this conjecture for surfaces with geometric genus greater than one is true (see [Lat18a], [Lat19]). There is also an analogous version of the conjecture for higher dimensional varieties, which is studied in [Voi96], [Lat16b], [Lat17], [Lat18c], [BLP17], [LV17], [Via18], [Bur18].…”

Zero-cycles on Cancian–Frapporti surfaces

“…As for geometric genus 1, Voisin's conjecture is still open for a general K3 surface; examples of surfaces of geometric genus 1 verifying the conjecture are given in [33], [15], [17], [18]. Examples of surfaces with geometric genus strictly larger than 1 verifying the conjecture are given in [21]. One can also formulate versions of conjecture 1.1 for higher-dimensional varieties; this is studied in [33], [16], [19], [20], [3], [22], [32], [6].…”