39 citations · 232 across the 70 of their papers we have counts for
19 papers · 1 filter
Algebraic cycles and EPW cubes
Robert Laterveer
Let be a hyperkähler variety with an anti-symplectic involution . According to Beauville's conjectural "splitting property", the Chow groups of should split in a finite…
Algebraic cycles on a very special EPW sextic
Robert Laterveer
Motivated by the Beauville-Voisin conjecture about Chow rings of powers of surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of…
Algebraic cycles on certain hyperkaehler fourfolds with an order non-symplectic automorphism
Robert Laterveer
Let be a hyperkähler variety, and assume has a non-symplectic automorphism of order . Bloch's conjecture predicts that the quotient should ha…
On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
Robert Laterveer, Charles Vial
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…
On complete intersections in varieties with finite-dimensional motive
Robert Laterveer, Jan Nagel, Chris Peters
Let be a complete intersection inside a variety with finite dimensional motive and for which the Lefschetz-type conjecture holds. We show how conditions on the nivea…
Some Calabi-Yau fourfolds verifying Voisin's conjecture
Robert Laterveer
Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning the behaviour of zero-cycles on self-products of Calabi-Yau varieties. This note contains some…
On Voisin's conjecture for zero-cycles on hyperkaehler varieties
Robert Laterveer
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 th…
Some cubics with finite-dimensional motive
Robert Laterveer
This small note presents in any dimension a family of cubics that have finite-dimensional motive (in the sense of Kimura). As an illustration, we verify a conjecture of Voevodsky f…
A family of cubic fourfolds with finite-dimensional motive
Robert Laterveer
We prove that cubic fourfolds in a certain 10-dimensional family have finite-dimensional motive. The proof is based on the van Geemen-Izadi construction of an algebraic Kuga-Satake…
The generalized Franchetta conjecture for some hyper-Kähler varieties
Lie Fu, Robert Laterveer, Charles Vial +1
The generalized Franchetta conjecture for hyper-Kähler varieties predicts that an algebraic cycle on the universal family of certain polarized hyper-Kähler varieties is fiberwise r…
Algebraic cycles on Fano varieties of some cubics
Robert Laterveer
This note is about cycle-theoretic properties of the Fano variety of lines on a smooth cubic fivefold. The arguments are based on the fact that this Fano variety has finite-dimensi…
Bloch's conjecture for Enriques varieties
Robert Laterveer
Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group o…
A remark on the Chow ring of some hyperkähler fourfolds
Robert Laterveer
Let be a hyperkähler variety. Voisin has conjectured that the classes of Lagrangian constant cycle subvarieties in the Chow ring of should lie in a subring injecting into c…
A remark on Beauville's splitting property
Robert Laterveer
Let be a hyperkähler variety. Beauville has conjectured that a certain subring of the Chow ring of should inject into cohomology. This note proposes a similar conjecture fo…
Voisin's Conjecture for Zero--cycles on Calabi--Yau Varieties and their Mirrors
Gilberto Bini, Robert Laterveer, Gianluca Pacienza
We study a conjecture, due to Voisin, on 0-cycles on varieties with . Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)Künneth de…
On the Chow groups of some hyperkähler fourfolds with a non-symplectic involution
Robert Laterveer
This note concerns hyperkähler fourfolds having a non-symplectic involution . The Bloch-Beilinson conjectures predict the way should act on certain pieces of the Chow gr…
Algebraic cycles on some special hyperkähler varieties
Robert Laterveer
This note contains some examples of hyperkähler varieties having a group of non-symplectic automorphisms, and such that the action of on certain Chow groups of is a…
About Chow groups of certain hyperkähler varieties with non-symplectic automorphisms
Robert Laterveer
Let be a hyperkähler variety, and let be a group of finite order non-symplectic automorphisms of . Beauville's conjectural splitting property predicts that each Chow gro…
On the Chow groups of certain cubic fourfolds
Robert Laterveer
This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold in the family has an inv…