相关论文: The Chow ring of punctual Hilbert schemes of toric…

We consider the bit complexity of computing Chow forms and their generalization to multiprojective spaces. We develop a deterministic algorithm using resultants and obtain a single exponential complexity upper bound. Earlier computational…

The purpose of this paper is to study the Zariski tangent space of the punctual Hilbert scheme parametrizing subschemes of a smooth surface which are supported at a single point. We give a lower bound on the dimension of the tangent space…

We compute the integral Chow ring of the moduli stack of smooth elliptic curves with $n$ marked points for $3\leq n\leq 10$.

We prove that there is an algorithm to compute the class of the intersection of the divisor of schemes incident to a fixed line with any other class of a basis of the Chow ring $A^*(\mathbb{P}^{2[N]})$ due to Mallavibarrena and Sols. This…

We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, we construct via combinatorial data in the Cox…

We prove that any element in the Chow ring of the Hilbert scheme $\text{Hilb}_n$ of $n$ points on a smooth surface $S$ is a universal class, i.e. the pushforward of a polynomial in the Chern classes of the universal subscheme on…

We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…

In this paper we give a complete description of the integral Chow ring of the stack $\mathscr{H}_{g,1}$ of 1-pointed hyperelliptic curves, lifting relations and generators from the Chow ring of $\mathscr{H}_g$. We also give a geometric…

Let X be an algebraic projective variety in {\bf P}^n. Denote by {\cal C}_{\lambda} the space of all effective cycles on X whose homology class is \lambda \in H_{2p} (X,{\bf Z}). It is easy to show that {\cal C}_{\lambda} is an algebraic…

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.

Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up…

The torus T of projective space also acts on the Hilbert scheme of subschemes of projective space. The T-graph of the Hilbert scheme has vertices the fixed points of this action, and edges connecting pairs of fixed points in the closure of…

In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample. This method…

Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces. Following Gel'fand, Kapranov and Zelevinsky, it decomposes into Chow forms of plane conics, Chow…

Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. We use families of curves on…

For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.

The rational Chow ring of the moduli space $\mathcal{M}_g$ of curves of genus $g$ is known for $g \leq 6$. Here, we determine the rational Chow rings of $\mathcal{M}_7, \mathcal{M}_8,$ and $\mathcal{M}_9$ by showing they are tautological.…

This paper gives computations of all the $G$-theory groups of several classes of simplicial toric varieties, including all affine toric surfaces when the base field is algebraically closed and has characteristic zero, all weighted…

G\"ottsche and Soergel gave formulas for the Hodge numbers of Hilbert schemes of points on a smooth algebraic surface and the Hodge numbers of generalized Kummer varieties. When a smooth projective surface $S$ admits an action by a finite…

For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G be the group of automorphisms of K[[x,y]] sending the ideal…