相关论文: Some Calabi-Yau fourfolds verifying Voisin's conje…

Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of hyperk\"ahler varieties, and we prove this…

Informed by the Bloch-Beilinson conjectures, Voisin has made a conjecture about $0$-cycles on self-products of Calabi-Yau varieties. In this note, we consider variant versions of Voisin's conjecture for cubic fourfolds, and for…

We study a conjecture, due to Voisin, on 0-cycles on varieties with $p_g=1$. Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)K\"unneth decomposition, we provide a general criterion for Calabi-Yau…

Inspired by the Bloch-Beilinson conjectures, Voisin has formulated a conjecture concerning the behaviour of 0-cycles on self-products of varieties of geometric genus one. This note presents some new examples of surfaces for which Voisin's…

An old conjecture of Voisin describes how zero-cycles on a variety $X$ should behave when pulled-back to the self-product $X^m$ for $m$ larger than the geometric genus of $X$. Using complete intersections of quadrics, we give examples of…

We consider Calabi-Yau $n$-folds $X$ arising from certain hyperplane arrangements. Using Fu-Vial's theory of distinguished cycles for varieties with motive of abelian type, we show that the subring of the Chow ring of $X$ generated by…

We study some conjectures about Chow groups of varieties of geometric genus one. Some examples are given of Calabi-Yau threefolds where these conjectures can be verified, using the theory of finite-dimensional motives.

A conjecture of Voisin states that two points on a smooth projective complex variety whose algebra of holomorphic forms is generated in degree 2 are rationally equivalent to each other if and only if their difference lies in the third step…

Gross-Joyce-Tanaka arXiv:2005.05637 proposed a wall-crossing conjecture for Calabi-Yau fourfolds. Assuming it, we prove the conjecture of Cao-Kool arXiv:1712.07347 for 0-dimensional sheaf-counting invariants on projective Calabi-Yau…

This note is about certain locally complete families of Calabi-Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle class map on the Chow ring of powers of these varieties…

In this paper, the generalized Bloch Conjecture on zero cycles for the quotient of certain complete intersections with trivial canonical bundle is proved to hold. As an application of Bloch-Srinivas method on the decomposition of the…

We construct Calabi-Yau manifolds and their mirrors from K3 surfaces. This method was first developed by Borcea and Voisin. We examined their properties torically and checked mirror symmetry for Calabi-Yau 4-fold case. From Borcea-Voisin…

In this note, an overview of Calabi-Yau varieties in positive characteristic is presented. Although Calabi-Yau varieties in characteristic zero are unobstructed, there are examples of Calabi-Yau threefolds in positive characteristic which…

This note is about an old conjecture of Voisin, which concerns zero--cycles on the self-product of surfaces of geometric genus one. We prove this conjecture for surfaces with $p_g=1$ and $q=2$.

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…

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…

We consider a conjecture of Kontsevich and Soibelman which is regarded as a foundation of their theory of motivic Donaldson-Thomas invariants for non-commutative 3d Calabi-Yau varieties. We will show that, in some certain cases, the answer…

In analogy with the Gopakumar-Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau 4-folds using Gromov-Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic…

We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally…

For a smooth projective variety X, let CH(X) be the Chow ring (with rational coefficients) of algebraic cycles modulo rational equivalence. The conjectures of Bloch and Beilinson predict the existence of a functorial ring filtration of…