Related papers: Relative Hilbert Scheme of Points

Let S be a smooth projective surface, and consider the following two subvarieties of the Hilbert scheme parameterizing closed subschemes of S of length n: A = {subschemes with support in a fixed point of S} B = {subschemes with support in…

We provide a criterion for when Hilbert schemes of points on K3 surfaces are birational. In particular, this allows us to generate a plethora of examples of non-birational Hilbert schemes which are derived equivalent.

Punctual noncommutative Hilbert schemes are projective varieties parametrizing finite codimensional left ideals in noncommutative formal power series rings. We determine their motives and intersection cohomology, by constructing affine…

We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture…

We determine the class of the Hilbert scheme of points on a surface in the Grothendieck group of varieties. As a corollary we obtain its class in the Grothendieck group of motives. We give some applications to moduli spaces of sheaves on…

The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such…

This is an announcement of conjectures and results concerning the generating series of Euler characteristics of Hilbert schemes of points on surfaces with simple (Kleinian) singularities. For a quotient surface C^2/G with G a finite…

The Hilbert scheme X^{[a]} of points on a complex manifold X is a compactification of the configuration space of a-element subsets of X. The integral cohomology of X^{[a]} is more subtle than the rational cohomology. In this paper, we…

Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3,…

In this paper, we introduce the concept of a relative Heffter space which simultaneously generalizes those of relative Heffter arrays and Heffter spaces. Given a subgroup $J$ of an abelian group $G$, a relative Heffter space is a resolvable…

In this paper we construct $G$-Hilbert schemes for finite group schemes $G$. We find a construction of $G$-Hilbert schemes as relative $G$-Hilbert schemes over the quotient that does not need the Hilbert scheme of $n$ points, works under…

We study the existence and the schematic structure of elementary components of the nested Hilbert scheme on a smooth quasi-projective variety. Precisely, we find a new lower bound for the existence of non-smoothable nestings of fat points…

In this paper we study monomial multiple structures on a linear subspace of codimension two in projective space. We show that these structures determine smooth points in their respective Hilbert schemes, with (smooth) neighbourhoods of two…

Let $\mathrm{Hilb}_nS$ be the Hilbert scheme of $n$ points on a smooth projective surface $S$. To a class $\alpha\in K^0(S)$ correspond a tautological vector bundle $\alpha^{[n]}$ on $\mathrm{Hilb}_nS$ and line bundle $L_{(n)}\otimes…

In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of $(1,k)$-quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric…

In this paper we study the Hilbert scheme, Hilb(P), of equidimensional locally Cohen-Macaulay codimension 2 subschemes, with a special look to surfaces in P^4 and 3-folds in P^5, and the Hilbert scheme stratification H_{c} of constant…

G\"ottsche gave a formula for the dimension of the cohomology of Hilbert schemes of points on a smooth projective surface $S$. When $S$ admits an action by a finite group $G$, we describe the action of $G$ on the Hodge structure. In the…

We compute an explicit closed formula for the Hilbert polynomial of the Jacobian algebra $M(f)$ of a reduced surface $X:f=0$ in $\mathbb P^3$ in terms of the graded Betti numbers of the algebra $M(f)$. When $X$ has only isolated…

We will construct a non-separable Hilbert space for which the inhomogeneous ${\rm SL}(2,\mathbb{C})$ acts on it unitarily. Each vector in this Hilbert space is described by a (rectangular) space-like surface in $\mathbb{R}^4$, for which a…

Let $S$ be a smooth projective surface with $p_g=q=0$. We show how to use derived categorical methods to study the geometry of certain special iterated Hilbert schemes associated to $S$ by showing that they contain a smooth connected…