Related papers: The Chow rings of $G_2$ and $Spin_7$

Given a sequence of point and rational curve blow-ups blow-ups of smooth $3-$dimensional projective varieties $Z_{i}$ defined over an algebraically closed field $\mathit{k}$, $Z_{s}\xrightarrow{\pi_{s}}…

The purpose of this second part of the series is to show a technical result on Chow groups of toric varieties. This is a crucial ingredient for the first part.

All curves on a separably rationally connected variety are rationally equivalent to a (non-effective) integral sum of rational curves, hence the first Chow group is generated by rational curves. Applying the same techniques, we also proved…

This article is about hyperk\"ahler fourfolds $X$ admitting a non-symplectic involution $\iota$. The Bloch-Beilinson conjectures predict the way $\iota$ should act on certain pieces of the Chow groups of $X$. The main result is a…

In this exposition we understand when the natural map from the Chow variety parametrizing codimension $p$ cycles on a smooth projective variety $X$ to the Chow group $\CH^p(X)$ is surjective. We derive some consequences when the map is…

In this paper we compute the integral Chow ring of the moduli space of stable elliptic curves with three marked points by combining several patching techniques, including higher Chow groups with $\ell$-adic coefficients.

Let $X$ be an affine, simplicial toric variety over a field. Let $G_0$ denote the Grothendieck group of coherent sheaves on a Noetherian scheme and let $F^1G_0$ denote the first step of the filtration on $G_0$ by codimension of support.…

We collect together various facts about G_2 and Spin(7) geometry which are likely well known but which do not seem to have appeared explicitly in the literature before. These notes should be useful to graduate students and new researchers…

Let M_{g,n} be the moduli space of stable genus g curves with n marked points. M_{g,n} has boundary strata consisting of nodal curves. The fundamental classes of these boundary strata may be linearly dependent in the Chow group…

The article considers the procedure of connection of graphs to the edges of a cyclic graph and its influence on the sandpile group of the graph thus obtained. A series of classes of graphs CH_n(a_1,...,a_n) is defined. Recurrent and…

For any vector bundle $V$ on a toric Deligne-Mumford stack $\ix$ the formalism of \cite{EJK:16} defines two intertial products $\star_{V^{+}}$ and $\star_{V^{-}}$ on the Chow group of the inertia stack. We give an explicit presentation for…

We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow groups of orders in global fields and show that there are…

In this paper we define a descending filtration on the Chow group of zero cycles for varieties of the form $A \times C_1 \times \cdots \times C_d$ where $A$ is an abelian variety and each $C_i$ is a smooth projective curve. We give explicit…

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…

Using a codimension-$1$ algebraic cycle obtained from the Poincar\'e line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow…

Oriented cohomology theories provide a general framework to perform intersection-theory-type calculus. The Chow ring, algebraic $K$-theory, and Levine--Morel's algebraic cobordism are all instances of such theories satisfying $\mathbb…

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"ahler algebraic varieties. Namely we prove in a number of cases that polynomial cohomological relations involving only CH^1(X) and the Chern classes of…

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…

We study classes of strata of differentials with fixed spin parity in the Chow ring of moduli spaces of curves. We show that these classes are tautological and computable. Furthermore, we establish the refined DR cycle formula for these…

Let H(d) be the (open) Hilbert scheme of rational normal curves of degree d in P^d. A presentation of the integral Chow ring of H(d) is given via equivariant Chow ring computations. Included also in the paper are algebraic computations of…