Related papers: Rational singularities of nested Hilbert schemes

The criterion for an affine primary algebra over the field to be integral, is proven. Using this criterion we give a simple proof that Hilbert scheme of 0-dimensional subschemes of length $l$ of nonsingular $d$-dimensional algebraic variety…

The Hilbert scheme of n points in the projective plane parameterizes degree n zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying…

We study symplectic resolutions of the Hilbert scheme of two points on a surface with one ADE-singularity. We also characterize such singularities by central fibers of their symplectic resolutions. As an application, we show that these…

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity…

A simply connected topological space is called \emph{rationally elliptic} if the rank of its total homotopy group and its total (co)homology group are both finite. A well-known Hilali conjecture claims that for a rationally elliptic space…

A continuous map $\mathbb{C}^n\to Gr(\tau, N)$ is $k$-regular if the $\tau$-dimensional subspaces corresponding to images of any $k$ distinct points span a $\tau k$-dimensional space. For $\tau = 1$ this essentially recovers the classical…

We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and observe that it is, in general, not determined solely by the Hochschild cohomology of the surface, but by its "Hochschild-Serre cohomology": the bigraded…

We characterize complete intersection matrix Schubert varieties, generalizing the classical result on one-sided ladder determinantal varieties. We also give a new proof of the F-rationality of matrix Schubert varieties. Although it is known…

We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.

Let $X$ be the projective plane, a Hirzebruch surface, or a general $K3$ surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on $X$. We…

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…

Let k be an algebraically closed field of characteristic 0. The question of irreducibility of the punctual Hilbert scheme Hilb_d P^n and its Gorenstein locus for various d was studied in [CEVV8, CN9, CN10, CN11]. In this short paper we…

We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. Denoting by $\mathcal{M}_g$ the moduli space of smooth curves of genus $g$, let $\mu: \mathcal{H}_{d,g,r}\dasharrow…

Mark Haiman has reduced Macdonald positivity conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjectures where the symmetric group is replaced by the wreath…

The Computational Algebraic Geometry applied in Algebraic Statistics; are beginning to exploring new branches and applications; in artificial intelligence and others areas. Currently, the development of the mathematics is very extensive and…

Let X be the quasi-projective symplectic surface that is given by the total space of the invertible sheaf O(-2) over the projective line. Let Hilb X be the family of Hilbert schemes of points on X. We give and prove a closed formula…

For the completion B of a local geometric normal domain, V. Srinivas asked which subgroups of Cl B arise as the image of the map from Cl A to Cl B on class groups as A varies among normal geometric domains with B isomorphic to the…

We study lines and twisted cubics on cubic fourfolds with simple isolated singularities. We show that the Hilbert scheme compactification of the total space of Starr's fibration on the space of twisted cubics on a cubic fourfold with simple…

Let $ G = \mathbb{Z}/r\mathbb{Z}$ be the cyclic group of order $r$, and let $\varpi = e^{2\pi i / r}$ denote a primitive $r$ th root of unity. Consider the action of $G$ on $\mathbb{C}^n$ via the embedding $$ \varphi : G \hookrightarrow…