Related papers: Smooth Hilbert schemes: their classification and g…
We give an algorithm to determine whether a kernel sheaf over a smooth projective curve over an algebraically closed field is semistable. The algorithm uses symmetric powers to make destabilizing subbundles visible as global sections.
We represent algebraic curves via commuting matrix polynomials. This allows us to show that the Hilbert scheme of cohomologically stable twisted rational curves of degree $d$ in ${\Bbb P}^3\backslash {\Bbb P}^1$ is isomorphic to a…
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
The space of subvarieties of P^n with a fixed Hilbert polynomial is not complete. Grothendieck defined a completion by relaxing "variety" to "scheme", giving the complete_Hilbert scheme_ of subschemes of P^n with fixed Hilbert polynomial.…
The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement,…
We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the limit we obtain the formulas for the…
Let $k$ be an algebraically closed field of characteristic zero and let $A$ be a finitely generated $k-$algebra. The Nori - Hilbert scheme of $A$, parameterizes left ideals of codimension $n$ in $A,$ and it is well known to be smooth when…
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
A Hilbert space frame on $R^n$ is {\it scalable} if we can scale the vectors to make them a tight frame. There are known classifications of scalable frames. There are two basic questions here which have never been answered in any $R^n$:…
The Hilbert scheme $X^{[3]}$ of length-$3$ subschemes of a smooth projective variety $X$ is known to be smooth and projective. We investigate whether the property of having a multiplicative Chow-Kuenneth decomposition is stable under taking…
We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine…
The sets of closed and closed-normal subgroups of a profinite group carry a natural profinite topology. Through a combination of algebraic and topological methods the size of these subgroup spaces is calculated, and the spaces partially…
Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
Consider a family of integral complex locally planar curves. We show that under some assumptions on the basis, the relative nested Hilbert scheme is smooth. In this case, the decomposition theorem of Beilinson, Bernstein and Deligne asserts…
In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept of consistent implicit maps, to generalize the symplecticity…
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…