39 citations · 232 across the 70 of their papers we have counts for
96 papers
Algebraic cycles and Fano threefolds of genus 7
Robert Laterveer
Let be a very general prime Fano threefold of genus 7. We exhibit an explicit 2-cycle on that is Abel-Jacobi trivial but non-torsion in the Chow group $A^4(Y\times…
Variation on a theme of Beauville-Voisin
Robert Laterveer
The Beauville-Voisin conjecture is about the Chow ring of hyper-Kähler varieties. We consider a variant version taking place in the ring of algebraic cycles modulo algebraic equiva…
A strong version of the Beauville-Voisin conjecture for certain hyper-Kähler fourfolds
Robert Laterveer
A strong version of the Beauville-Voisin conjecture asserts that for hyper-Kähler varieties, the subring of the Chow ring generated by divisors, Chern classes and Lagrangian consta…
Questions on the Chow ring of complete intersections
Robert Laterveer
We state several questions, and prove some partial results, about the Chow ring of complete intersections in projective space. For one thing, we prove that if is a…
Double EPW sextics and the Voisin filtration on zero-cycles
Michele Bolognesi, Robert Laterveer
Let be a double EPW sextic, and its anti-symplectic involution. We relate the -anti-invariant part of the Chow group of zero-cycles of with Voisin's rational orbit f…
Zero-cycles and the Cayley-Oguiso automorphism
Gilberto Bini, Robert Laterveer
Cayley and Oguiso have constructed certain quartic K3 surfaces , with automorphisms of infinite order. We show that when is symplectic (resp. anti-symplectic), it acts a…
The Beauville-Voisin-Franchetta conjecture and LLSS eightfolds
Robert Laterveer, Charles Vial
The Chow rings of hyper-Kähler varieties are conjectured to have a particularly rich structure. In this paper, we formulate a conjecture that combines the Beauville-Voisin conjectu…
A 9-dimensional family of K3 surfaces with finite dimensional motive
Michele Bolognesi, Robert Laterveer
Let S be a K3 surface obtained as triple cover of a quadric branched along a genus 4 curve. Using the relation with cubic fourfolds, we show that S has finite dimensional motive, i…
The Beauville-Voisin conjecture for double EPW sextics
Robert Laterveer
We prove that the Beauville-Voisin conjecture is true for any double EPW sextic, i.e. the subalgebra of the Chow ring generated by divisors and Chern classes of the tangent bundle…
Algebraic cycles and Fano threefolds of genus 10
Robert Laterveer
We show that prime Fano threefolds of genus 10 have a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of…
Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
Giuseppe Ancona, Mattia Cavicchi, Robert Laterveer +1
We show that the hyper-Kähler varieties of OG10-type constructed by Laza-Saccà-Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general resul…
Some more Fano threefolds with a multiplicative Chow-Künneth decomposition
Robert Laterveer
We exhibit several families of Fano threefolds with a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the…
On the tautological ring of Humbert curves
Robert Laterveer
We exhibit a 2-dimensional family of non-hyperelliptic curves of genus 5, called Humbert curves, for which the tautological ring injects into cohomology. In particular, Humbert cur…
On the Chow Ring of Fano Fourfolds of K3 type
Michele Bolognesi, Robert Laterveer
We show that a wide range of Fano varieties of K3 type, recently constructed by Bernardara, Fatighenti, Manivel and Tanturri, have a multiplicative Chow-Künneth decomposition, in t…
Some Motivic Properties of Gushel-Mukai Sixfolds
Michele Bolognesi, Robert Laterveer
Gushel-Mukai sixfolds are an important class of so-called Fano-K3 varieties. In this paper we show that they admit a multiplicative Chow-Künneth decomposition modulo algebraic equi…
Special cubic fourfolds, K3 surfaces and the Franchetta property
Lie Fu, Robert Laterveer
O'Grady conjectured that the Chow group of 0-cycles of the generic fiber of the universal family over the moduli space of polarized K3 surfaces of genus g is cyclic. This so-called…
Some new Fano varieties with a multiplicative Chow-Künneth decomposition
Robert Laterveer
Let be a smooth dimensionally transverse intersection of the Grassmannian with 3 Plücker hyperplanes. We show that admits a multiplicative Chow-Künneth dec…
Algebraic cycles and Fano threefolds of genus 8
Robert Laterveer
We show that prime Fano threefolds of genus 8 have a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of t…
Algebraic cycles and Lehn-Lehn-Sorger-van Straten eightfolds
Robert Laterveer
This article is about Lehn-Lehn-Sorger-van Straten eightfolds , and their anti-symplectic involution . When is birational to the Hilbert scheme of points on a K3 surface,…
Algebraic cycles and intersections of three quadrics
Robert Laterveer
Let be a smooth complete intersection of three quadrics, and assume the dimension of is even. We show that has a multiplicative Chow-Künneth decomposition, in the sense…
On the Chow ring of Fano varieties on the Fatighenti-Mongardi list
Robert Laterveer
Conjecturally, Fano varieties of K3 type admit a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. We prove this for many of the families of Fano varieties of K…
Algebraic cycles and intersections of 2 quadrics
Robert Laterveer
A smooth intersection of two quadrics in has Hodge level 1. We show that such varieties have a multiplicative Chow-Künneth decomposition, in the sense o…
On the Chow ring of some Lagrangian fibrations
Robert Laterveer
Let be a hyperkähler variety admitting a Lagrangian fibration. Beauville's "splitting property" conjecture predicts that fibres of the Lagrangian fibration should have a partic…
On the motive of codimension 2 linear sections of
Robert Laterveer
We consider Fano sevenfolds obtained by intersecting the Grassmannian with a codimension 2 linear subspace (with respect to the Plücker embedding). We prove th…