Abstract In this paper, we prove a decomposition result for the Chow groups of projectivizations coherent sheaves homological dimension $\le 1$ . process, establish cases Cayley trick and standard flips. Moreover, apply these results to study symmetric powers curves, nested Hilbert schemes surfaces, varieties resolving Voisin maps cubic fourfolds.

Let $Y$ be a smooth complete intersection of three quadrics, and assume the dimension is even. We show that has multiplicative Chow-K\"unneth decomposition, in sense Shen-Vial. As consequence, Chow ring (powers of) displays K3-like behaviour. by-product argument, we also establish decomposition for double planes.

We study additive higher Chow groups with several modulus conditions. Apart from exhibiting the validity of all known results for the additive Chow groups with these modulus conditions, we prove the moving lemma for them: for a smooth projective variety X and a finite collection W of its locally closed algebraic subsets, every additive higher Chow cycle is congruent to an admissible cycle inter...

Intermittent, extended access to preferred diets increases their intake. However, the effects of such access on the acceptance and reinforcing efficacy of otherwise satisfying alternatives is less known. To investigate the role of nonnutritional contributions to the hypophagia that follows removal of preferred food, male Wistar rats were fed a chow diet (Chow A/I), preferred to their regular ch...

Especially notable here is Spencer Bloch’s semi-regularity paper [B]. The advantage of this approach is that one can use the full strength of the deformation theory of subvarieties. One might similarly ask whether there is a family of algebraic cycles {Zt}t∈B deforming Z; some first steps toward an infinitesimal theory for this problem were the subject of [G-G2]. A third possible context, which...

1.0 Properties of M0,n ⊂ M0,n. (1) M0,n has a natural moduli interpretation, namely it is the moduli space of stable n-pointed rational curves. (2) Given power series f1(z), . . . , fn(z) which we think of as a one parameter family in M0,n one can ask: What is the limiting stable n-pointed rational curve in M0,n as z → 0 ? There is a beautiful answer, due to Kapranov [Kapranov93a], in terms of ...

1.1. Principal G-bundles. Topology is concerned with topological spaces and continuous maps between them. But the data is a topological space of so complicated and infinite in nature that it can be very difficult even to tell when two topological spaces are “the same.” For instance, all n-dimensional manifolds look locally the same. A central theme in algebraic topology is to attach algebraic i...

This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.