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Algebraic cycles on surfaces with and
Robert Laterveer
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=…
Some elementary examples of quartics with finite-dimensional motive
Robert Laterveer
This small note contains some easy examples of quartic hypersurfaces that have finite-dimensional motive. As an illustration, we verify a conjecture of Voevodsky (concerning smash-…
Hard Lefschetz for Chow groups of generalized Kummer varieties
Robert Laterveer
The main result of this note is a hard Lefschetz theorem for the Chow groups of generalized Kummer varieties. The same argument also proves hard Lefschetz for Chow groups of Hilber…
A remark on the motive of the Fano variety of lines of a cubic
Robert Laterveer
Let be a smooth cubic hypersurface, and let be the Fano variety of lines on . We establish a relation between the Chow motives of and . This relation implies in p…
Algebraic cycles and Todorov surfaces
Robert Laterveer
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 f…
Some new examples of smash-nilpotent algebraic cycles
Robert Laterveer
Voevodsky has conjectured that numerical equivalence and smash-equivalence coincide for algebraic cycles on any smooth projective variety. Building on work of Vial and Kahn-Sebasti…
On a multiplicative version of Bloch's conjecture
Robert Laterveer
A theorem of Esnault, Srinivas and Viehweg asserts that if the Chow group of 0-cycles of a smooth complete complex variety decomposes, then the top-degree coherent cohomology group…
A note about connectedness theorems a la Barth
Robert Laterveer
We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain "easy" ambient spaces (such as homogeneous varieties…
Some results on a conjecture of Voisin for surfaces of geometric genus one
Robert Laterveer
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…
Some remarks on cones of partially ample divisors
Robert Laterveer
We study the cones of q-ample divisors on smooth complex varieties. In favourable cases, we identify a part where the closure of this cone and the nef cone have the same boundary.…
A family of K3 surfaces having finite-dimensional motive
Robert Laterveer
This short note contains an example of a 4-dimensional family of K3 surfaces having finite-dimensional motive. Some consequences are presented, for instance the verification of a c…
Some desultory remarks concerning algebraic cycles and Calabi--Yau threefolds
Robert Laterveer
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…
On a multiplicative version of Mumford's theorem
Robert Laterveer
A theorem of Esnault, Srinivas and Viehweg asserts that if the Chow group of 0-cycles of a smooth complete complex variety decomposes, then the top-degree coherent cohomology group…