Related papers: Zero-cycles on double EPW sextics

We show that the graded Chow rings of two birational irreducible symplectic varieties are isomorphic. This lifts a result known for the cohomology algebras to the level of Chow rings, despite the non-injectivity the cycle class map. In the…

We show that the Chow group of 0-cycles on a singular projective scheme $X$ over a finite field describes the abelian extensions of its function field which are unramified over the regular locus of $X$. As a consequence, we obtain the…

We study the Chow ring of the boundary of the partial compactification of the universal family of principally polarized abelian varieties (ppav). We describe the subring generated by divisor classes, and compute the class of the partial…

Under some hypotheses on the singular type of the one-parameter family of elliptic curves in a primitively polarized $K3$ surface $S$ determined by its polarization (which is expected to be true for a very general polarized $K3$ surface),…

Let X be a K3 surface. We show that the Chow group CH_0(X) of 0-cycles contains a "fundamental class" c_X of degree 1 with remarkable properties: any product of divisors is proportional to this class, and so is the second Chern class…

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of…

A $K3$ surface with an ample divisor of self-intersection 2 is a double cover of the plane branched over a sextic curve. We conjecture that a similar statement holds for the generic couple $(X,H)$ with $X$ a deformation of $(K3)^{[n]}$ and…

We prove several results about integral versions of Fourier duality for abelian schemes, making use of Pappas's work on integral Grothendieck-Riemann-Roch. If $S$ is smooth quasi-projective of dimension $d$ over a field and $\pi \colon X\to…

Let $X$ be a hyperk\"ahler variety. Voisin has conjectured that the classes of Lagrangian constant cycle subvarieties in the Chow ring of $X$ should lie in a subring injecting into cohomology. We study this conjecture for the Fano variety…

Let $Y$ be a smooth complete intersection of a quadric and a cubic in $\mathbb{P}^n$, with $n$ even. We show that $Y$ has a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers…

This article is about Lehn-Lehn-Sorger-van Straten eightfolds $Z$, and their anti-symplectic involution $\iota$. When $Z$ is birational to the Hilbert scheme of points on a K3 surface, we give an explicit formula for the action of $\iota$…

Let $Y$ be a smooth complete intersection of three quadrics, and assume the dimension of $Y$ is even. We show that $Y$ has a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers…

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1$ branched over $n+2$ points. We prove that for a very…

We study the deformations of the Chow group of zero-cycles of the special fibre of a smooth scheme over a henselian discrete valuation ring. Our main tools are Bloch's formula and differential forms. As a corollary we get an algebraization…

Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple…

We prove a restriction isomorphism for Chow groups of zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore, we study torsion subgroups of these groups…

Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective…

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a certain family of surfaces, which are constructed by a product of certain hypergeometric curves of degree $N$. We prove that for a very general member, these cycles are…

Let $X$ be a hyperk\"ahler variety, and assume $X$ has a non-symplectic automorphism $\sigma$ of order $>{1\over 2}\dim X$. Bloch's conjecture predicts that the quotient $X/<\sigma>$ should have trivial Chow group of $0$-cycles. We verify…

In the present paper we introduce the property AA of a subsemigroup of the endomorphism semigroup of an abelian variety, which holds for semigroup of endomorphisms of an abelian variety defined over a number field, and show that the orbit…