Related papers: The Chow of $S^{[n]}$ and the universal subscheme

Let S be a smooth projective surfaces and S^[n] the Hilbert scheme of zero-dimensional subschemes of S of length n. We proof that the class of S^[n] in the complex cobordism ring depends only on the class of the surface itself. Moreover, we…

We show that tautological integrals on Hilbert schemes of points can be written in terms of universal polynomials in Chern numbers. The results hold in all dimensions, though they strengthen known results even for surfaces by allowing…

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…

The rational Chow ring A?(S[n],Q) of the Hilbert scheme S[n] parametrising the length n zero-dimensional subschemes of a toric surface S can be described with the help of equivariant techniques. In this paper, we explain the general method…

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…

Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution…

We show the existence of a regular universal quotient as a smooth commutative algebraic group of the Chow group of 0-cycles on a projective reduced variety, and give over the field of complex numbers an analytic description of it. This…

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on…

Let $S$ be a smooth projective surface over $\mathbb{C}$ and $S^{[n]}$ be the Hilbert scheme of $n$ points over $S$, for any positive integer $n$. Let ${\bf a}=(n_1,\ldots,n_r)$ and ${\bf b}=(m_1,\ldots,m_s)$ be two distinct partitions of…

Given a smooth projective variety $X$ over an algebraically closed field $k$, we compute the Chow ring of the Hilbert scheme of three points on $X$, $\operatorname{Hilb}^3(X)$, as an algebra with generators and relations over the Chow ring…

The Beauville-Voisin conjecture for a hyperk\"ahler manifold X states that the subring of the Chow ring A^*(X) generated by divisor classes and Chern characters of the tangent bundle injects into the cohomology ring of X. We prove a weak…

We prove in this paper the smoothability of cycles modulo rational equivalence in the Whitney range, that is, when the dimension is strictly smaller than the codimension. We introduce and study the class of cycles obtained as ``flat…

We prove that Chow groups of certain non-commutative Hilbert schemes have a basis consisting of monomials in Chern classes of the universal bundle. Furthermore, we realize the cohomology of non-commutative Hilbert schemes as a module over…

We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper.…

Following Mumford and Chiodo, we compute the Chern character of the derived pushforward $\textrm{ch} (R^\bullet\pi_\ast\mathscr{O}(\mathsf{D}))$, for $\mathsf D$ an arbitrary element of the Picard group of the universal curve over the…

The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for…

Let $S$ be the affine plane regarded as a toric variety with an action of the 2-dimensional torus $T$. We study the equivariant Chow ring $A_{K}^*(Hilb^n(S))$ of the punctual Hilbert scheme $Hilb^n(S)$ with equivariant coefficients…

Let X be a smooth projective toric surface, and H^d(X) the Hilbert scheme parametrising the length d zero-dimensional subschemes of X. We compute the rational Chow ring A^*(H^d(X))\_Q. More precisely, if T is the two-dimensional torus…

Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $X$ be an irreducible smooth projective surface over $k$. Fix an integer $n \geq 1$ and let ${\mathcal{H}{\it ilb}}_X^n$ be the Hilbert scheme parameterizing effective…

We fix the lexicographic order $\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define $\Hi^{\prec\Delta}_{S/k}$, the moduli space of reduced Gr\"obner bases with a given finite standard set $\Delta$, and its open…