Related papers: Chow groups of weighted hypersurfaces

Beauville and Voisin proved that the third modified diagonal of a complex K3 surface X represents a torsion class in the Chow group of X^3. Motivated by this result and by conjectures of Beauville and Voisin on the Chow ring of hyperkaehler…

A conjecture of Beauville and Voisin states that for an irreducible symplectic variety X, any polynomial relation between classes of divisors and the Chern classes of X which holds in cohomology already holds in the Chow groups. We verify…

We determine the Chow group of zero-cycles on a rational surface X defined over a finite extension K of the field of p-adic numbers (p a prime) when X is split by an unramified extension of K.

We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.

"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by…

We prove a Noether--Lefschetz-type result for certain linear systems on a projective threefold with isolated singularities.

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

We prove Viehweg's hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the the base space of a maximal variation family of smooth projective…

We prove analogs of Whitehead's theorem (from algebraic topology) for both the Chow groups and for the Grothendieck group of coherent sheaves: a morphism between smooth projective varieties whose pushforward is an isomorphism on the Chow…

Second derivative pinching estimates are proved for a class of elliptic and parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply…

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a…

We study a notion of convex cocompactness for discrete subgroups of the projective general linear group acting (not necessarily irreducibly) on real projective space, and give various characterizations. A convex cocompact group in this…

A reciprocal linear space is the image of a linear space under coordinate-wise inversion. These fundamental varieties describe the analytic centers of hyperplane arrangements and appear as part of the defining equations of the central path…

In this paper, we investigate Murre's conjectures on the structure of rational Chow groups and exhibit explicit Chow--Kuenneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent…

In this article, we improve our main results from \emph{Chow groups and $L$-derivatives of automorphic motives for unitary groups} in two direction: First, we allow ramified places in the CM extension $E/F$ at which we consider…

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…

Flat surfaces that correspond to meromorphic $1$-forms or to meromorphic quadratic differentials containing poles of order two and higher are surfaces of infinite area. We classify groups that appear as Veech groups of translation surfaces…

Given certain intersection cohomology sheaves on a projective variety with a torus action, we relate the cohomology groups of their tensor product to the cohomology groups of the individual sheaves. We also prove a similar result in the…

We adapt for algebraically closed fields $k$ of characteristic greater than $2$ two results of Voisin, on the decomposition of the diagonal of a smooth cubic hypersurface $X$ of dimension $3$ over $\mathbb C$, namely: the equivalence…