Related papers: Bloch's conjecture for the surface of Craighero an…
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…
Let $S$ be a smooth projective surface with $p_g=0$, let $\iota $ be a regular involution acting on $S$, and let $W$ be the resolution of singularities of the quotient surface $S/\iota $. In the paper we prove that Bloch's conjecture holds…
We prove Bloch's conjecture for numerical Campedelli surfaces with fundamental group of order $9$.
In this paper, we prove that Bloch's conjecture holds for all smooth, complex, projective surfaces with $p_g=q=0$ and $K^2=9$.
We prove that a recent construction of a numerical Godeaux surface due to P. Craighero and R. Gattazzo is simply connected, and show how to realize their construction as a double plane. By proving that the surface contains no (-2)-curves,…
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…
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…
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…
We consider the conjectures from the paper by Katzarkov, Kontsevich, and Pantev about Landau-Ginzburg Hodge numbers associated to tamely compactifiable Landau-Ginzburg models. We test these conjectures in case of dimension two, verifying…
In this paper, we prove the Bloch-Beilinson conjecture for certain abelian surfaces over $\mathbb{Q}$, provided that the BSD is known for these abelian surfaces.
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…
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.
We prove a special case of the Bloch-Kato conjecture for adjoint motives associated to modular abelian surfaces.
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.…
In this paper, we prove a conjecture of Schnell in the surface case.
Generalized Burniat surfaces are surfaces of general type with $p_g=q$ and Euler number $e=6$ obtained by a variant of Inoue's construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these…
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later we summarize the main ideas in the higher dimensional statement and…
We prove the conjecture stated by Spencer Bloch in 1975 and saying that the Albanese kernel of a smooth projective surface is 0, provided its second cohomology group is algebraic.
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 show that if the Atiyah Jones conjecture holds for a surface $X,$ then it also holds for the blow-up of $X$ at a point. Since the conjecture is known to hold for ${\mathbb P}^2$ and for ruled surfaces, it follows that the conjecture is…