Related papers: The Chow ring of Mbar_{0,m}(n, d)

We compute the Chow motive and the Chow groups with rational coefficients of the Hilbert scheme of points on a smooth algebraic surface

Motivic cohomology is powerful tool in algebraic geometry with associated realization maps giving important information about the relations between cohomological invariants of schemes and their classifying spaces. The problem of computing…

We introduce and compute the class of a number of effective divisors on the moduli space of stable maps $\bar M_{0,0}(P^{r},d)$, which, for small d, provide a good understanding of the extremal rays and the stable base locus decomposition…

The main goal of this paper is to define a certain Chow weight structure $w_{Chow}$ on the category $DM_c(S)$ of (constructible) $cdh$-motives over an equicharacteristic scheme $S$. In contrast to the previous papers of D. H\'ebert and the…

We compute the stringy chow ring of a general Deligne-Mumford stack of the form [X/G] for a smooth variety X and diagonalizable group scheme G, working over a base field that is not necessarily algebraically closed. We then specialize to…

We show that the ring of modular forms with characters for $\mathrm{O}(2,4;\mathbb{Z})$ is generated by forms of weights 4, 4, 6, 8, 10, 10, 12, and 30 with three relations of weights 8, 20, and 60. The proof is based on the study of a…

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…

In this paper, we construct toric data of moduli space of quasi maps of degree $d$ from P^{1} with two marked points to weighted projective space P(1.1,1,3). With this result, we prove that the moduli space is a compact toric orbifold. We…

This paper is the third and final part of a series devoted to the description of the integral Chow rings of the moduli stacks of hyperelliptic Prym pairs. For a fixed genus $g$, there are two natural stacks, $\mathcal{RH}_g$ and…

We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new formulas for the Poincar\'e polynomial of the moduli space…

We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…

This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces over the real numbers. In the study of the subvarieties of a projective algebraic variety, smooth over the field of real numbers, the cycle…

In this paper we compute the Chow--Witt rings of the classifying space ${\rm BSL}_n^c$ of quadratically oriented vector bundles of rank $n$. We also discuss the corresponding quadratically-oriented cobordism spectrum ${\rm MSL}^c$ and show…

The goal of this paper is to compute the rational Chow ring of the stack consisting of nodal curves of genus 0 with at most 3 nodes: it is a Q-algebra with 10 generators and 11 relations.

We compute the integral Chow ring of the stack of smooth, non-hyperelliptic curves of genus three. We obtain this result by computing the integral Chow ring of the stack of smooth plane quartics, by means of equivariant intersection theory.

In this paper certain Chow weight structures on the "big" triangulated motivic categories $DM_R^{eff}\subset DM_R$ are defined in terms of motives of all smooth varieties over the base field. This definition allows studying basic properties…

We study subrings in the Chow ring $\CH^*(A)_{{\Bbb Q}}$ of an abelian variety $A$, stable under the Fourier transform with respect to an arbitrary polarization. We prove that by taking Pontryagin products of classes of dimension $\leq 1$…

We prove two dual recursive decompositions as a graded $\underline{\mathrm{CH}}(M)\otimes \underline{\mathrm{CH}}(N)$-module of the Chow ring $\underline{\mathrm{CH}}(M\oplus N)$ of the direct sum of matroids. We use this to obtain a…

We construct the moduli space, $M_d$, of degree $d$ rational maps on $\mathbb{P}^1$ in terms of invariants of binary forms. We apply this construction to give explicit invariants and equations for $M_3$. Using classical invariant theory, we…

We consider free algebraic actions of the additive group of complex numbers on a complex vector space X embedded in the complex projective space. We find an explicit formula for the map p that assigns to a generic point x in X the Chow…