Related papers: Bloch's conjecture for surfaces with involutions a…

In this short note we prove that the Bloch's conjecture holds for a surface of general type of numerical Godeaux type or some class of numerical Campedelli type, with geometric genus zero equipped with an involution, when the quotient of…

In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0=q, K^2=3$, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such…

In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0$, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when…

We give many examples of surfaces of general type with $p_g=0$ for which Bloch's conjecture holds, for all values of $K^2$ except 9. Our surfaces are equipped with an involution.

In this paper, we prove that Bloch's conjecture holds for all smooth, complex, projective surfaces with $p_g=q=0$ and $K^2=9$.

Using recent developments in the theory of mixed motives, we prove that the log Bloch conjecture holds for an open smooth complex surface if the Bloch conjecture holds for its compactification. This verifies the log Bloch conjecture for all…

In this note we are going to consider a smooth projective surface equipped with an involution and study the action of the involution at the level of Chow group of zero cycles.

Catanese surfaces are regular surfaces of general type with $p_g=0$. They specialize to double covers of Barlow surfaces. We prove that the $CH_0$ group of a Catanese surface is equal to $\mathbb{Z}$, which implies the same result for the…

Bloch's conjecture for a surface $X$ over an algebraically closed field $k$ states that every homologically trivial correspondence $\Gamma $ acts as 0 on the Albanese kernel $T(X_{\Omega})$, where $\Omega $ is a universal domain containing…

For a smooth projective surface X the finite dimensionality of the Chow motive h(X), as conjectured by S.I Kimura, has several geometric consequences. For a complex surface of general type with p_g = 0 it is equivalent to Bloch's…

The aim of this article is to prove Bloch's conjecture (asserting that the group of rational equivalence classes of zero cycles of degree zero is trivial) for Inoue surfaces with p_g=0 and K^2 = 7. These surfaces can also be described as…

The goal of this paper is to prove Bloch's conjecture for the numerical Godeaux surface constructed by P. Craighero and R. Gattazzo.

In this note we prove that the Beilinson conjecture holds for certain examples of K3 surfaces over $\bar {\mathbb{Q}}$ equipped with an involution, when the quotient of the surface by the involution is the projective plane branched along a…

The aim of this article is to prove Bloch's conjecture, asserting that the group of rational equivalence classes of zero cycles of degree 0 is trivial for surfaces with geometric genus zero, for regular generalized Burniat type surfaces.…

Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homologically trivial idempotent in the ring of correspondences…

In this paper, we investigate Bloch's conjecture for autoequivalence on K3 surfaces. We introduce the notion of reflective autoequivalence of twisted K3 surfaces and prove Bloch's conjecture for such autoequivalences, thereby confirming the…

According to the Bloch-Beilinson conjectures, an automorphism of a K3 surface X that acts as the identity on the transcendental lattice should act trivially on CH^2(X). We discuss this conjecture for symplectic involutions and prove it in…

Symplectic involutions of a K3 surface are those involutions which leave the holomorphic 2-form invariant. We show, as predicted by Bloch's conjecture, that they act trivially on the CH_0 group of the K3 surface. This was recently proved by…

For a projective K3 surface X we introduce the dense triangulated subcategory S^* of the bounded derived category D^b(Coh(X)) of coherent sheaves on X that is generated by spherical objects. For a K3 surface X over \bar Q it is shown that…

We prove Bloch's conjecture for numerical Campedelli surfaces with fundamental group of order $9$.