Related papers: Hilbert schemes of some threefold scrolls over F_e
We study the Hilbert scheme $\mathcal{H}^\mathcal{L}_{d,g,r}$ parametrizing smooth, irreducible, non-degenerate and linearly normal curves of degree $d$ and genus $g$ in $\mathbb{P}^r$ whose complete and very ample hyperplane linear series…
We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\PP^r$. In this…
We consider the multigraded Hilbert scheme corresponding to the Hilbert function of a finite number of points in general position in a smooth projective complex toric variety. We develop several criteria for a point of that parameter space…
We work out details of the extrinsic geometry for two Hilbert schemes of some contemporary interest: the Hilbert scheme of two points on the projective plane and the dense open set parametrizing non-planar clusters in the punctual Hilbert…
As a continuation of the work of Freiermuth and Trautmann, we study the geometry of the moduli space of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $4m+1$. The moduli space has three irreducible components whose generic…
In this paper, we check that Fano schemes of lines on certain rational cubic fourfolds are birational to Hilbert schemes of two points on K3 surfaces.
We study locally Cohen-Macaulay curves of low degree in the Segre threefold with Picard number three and investigate the irreducible and connected components respectively of the Hilbert scheme of them. We also discuss the irreducibility of…
In a previous paper, a realization of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces in terms of monads was given. We build upon that result to construct ADHM data for the Hilbert scheme of points of the total space…
This is a survey article on moduli of affine schemes equipped with an action of a reductive group. The emphasis is on examples and applications to the classification of spherical varieties.
We study the component structures of some standard-graded Hilbert schemes closely related to a Hilbert scheme of curves studied by Gotzmann. In particular, we encounter examples of singular lex-segment points lying on two and three…
The new compactification of moduli scheme of Gieseker-stable vector bundles with the given Hilbert polynomial on a smooth projective polarized surface (S;H), over the field k = \bar k of zero characteristic, is constructed in previous…
This paper continues our researches \cite{DS1, DS2, DS3} by computing some invariants based on Hilbert-Poincar\'{e} series associated to Milnor algebras. Our computations are for some of the classical surfaces and 3-folds with different…
We compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a K\"ahler surface to the corresponding components of the Hilbert scheme, and show that they are isomorphic. Next we show how to compute the…
We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the…
This paper investigates Ulrich bundles on decomposable threefold scrolls X over the Hirzebruch surface $\mathbb F_a$, for any integer $a \geq 0$, focusing on the study of their structure and classification. We prove existence of such Ulrich…
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…
Hilbert specialization is an important tool in Field Arithmetic and Arithmetic Geometry, which has usually been intended for polynomials, hence hypersurfaces, and at scalar values. In this article, first, we extend this tool to prime…
We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings -- one way or the other -- between surfaces of section for the Hopf flow and those for any other Seifert fibration of…
We describe the natural geometry of Hilbert schemes of curves in ${\mathbb P}^3$ and, in some cases, in ${\mathbb P}^n$ , $n\geq 4$.
Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface $S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with $C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.