Related papers: Absolute Chow-Kuenneth decomposition for rational …

In this paper we investigate Murre's conjecture on the Chow--K\"unneth decomposition for two classes of examples. We look at the universal families of smooth curves over spaces which dominate the moduli space $\cM_g$, in genus at most 8 and…

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 paper, we show the existence of a Chow--Kuenneth decomposition for the moduli stack of stable curves of genus g with r marked points, for low values of g,r. We also look at the moduli space R of double covers of genus 3 curves,…

We discuss the existence of an absolute Chow-Kuenneth decomposition for complete degenerations of families of Abelian threefolds with complex multiplication over a particular Picard Modular Surface studied by Holzapfel. In addition to the…

Let $f : X \rightarrow B$ be a proper flat dominant morphism between two smooth quasi-projective complex varieties $X$ and $B$. Assume that there exists an integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) = \Q$ for…

We study the notion of a birational Chow-K\"unneth decomposition, which is essentially a decomposition of the integral birational motive of a variety. The existence of a birational Chow-K\"unneth decomposition is stably birationally…

Let $k$ be a field and let $\Omega$ be a universal domain over $k$. Let $f:X \r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $\leq 2$ such that the general…

Let X be the quotient of a smooth projective variety over a field by a finite group action (in which case we say X is pseudo-smooth), such that the singularities of X are isolated k-rational points. Let Y be obtained by blowing up these…

This article is about motives of quadric bundles. In the case of odd dimensional fibers and where the basis is of dimension two we give an explicit relative and absolute Chow-K\"unneth decomposition. This shows that the motive of the…

We construct a relative Chow-Kunneth decomposition for a conic bundle over a surface such that the middle projector gives the Prym variety of the associated double covering of the discriminant of the conic bundle. This gives a refinement…

We show that a smooth projective variety admits a Chow-Kunneth decomposition if the cohomology has level at most one except for the middle degree. This can be extended to the relative case in a weak sense if the morphism has only isolated…

We show that any nonconstant morphism of a threefold admits a relative Chow-Kuenneth decomposition. As a corollary we get sufficient conditions for threefolds to admit an absolute Chow-Kuenneth decomposition. In case the image of the…

In the present article we define an integral analogue of Chow-K\"unneth decomposition for \'etale motives. By using families of conservative functors we are able to establish a decomposition of the \'etale motive of commutative group…

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…

We consider a uniform $r$-bundle $E$ on a complex rational homogeneous space $X$ %over complex number field $\mathbb{C}$ and show that if $E$ is poly-uniform with respect to all the special families of lines and the rank $r$ is less than or…

We prove an absolute Chow-Kuenneth decomposition for the motive of universal families A of abelian varieties over some compact Shimura surface. We furthermore prove the Hodge conjecture for general fibres of A, extending results of Ribet.

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles and Ulrich bundles on rational homogeneous spaces. %with respect to general polarizations. From this result, we see that there are only finitely many…

In this article we prove the irreducibility of the Hilbert scheme of rationnal curves on homogeneous varieties with fixed class in the Chow ring. This result has also been proved by J. F. Thomsen [T] and B. Kim and R. Pandharipande [KP].…

The study of Chow varieties of decomposable forms lies at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. There are many open questions about homological properties of Chow varieties and…

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 decomposes similarly. In this note, we prove a similar…