相关论文: Murphy's Law for Hilbert function strata in the Hi…
Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. We show that if X is Frobenius split then so is the Hilbert scheme Hilb^n(X) of n points in X. In particular, we get the higher…
We present a sufficient condition for the punctural Hilbert scheme of length two of a K3 surface with finite automorphism group to have automorphism group of infinite order in geometric terms (Theorem 2.1). We then give concrete examples…
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…
In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a…
We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of association of special Hilbert spaces of functions, namely de…
Two approaches for determining Hilbert functions of fat point subschemes of $\mathbb P^2$ are demonstrated. A complete determination of the Hilbert functions which occur for 9 double points is given using the first approach, extending…
We prove that the Gorenstein locus of the Hilbert scheme of points on $\mathbb A^n$ is non-reduced for $n\geq 12$; we construct examples of non-reduced points that come from apolar algebras of the sum of general cubics. As a corollary, we…
We show that every automorphism of the Hilbert scheme of $n$ points on a weak Fano or general type surface is natural, i.e. induced by an automorphism of the surface, unless the surface is a product of curves and $n=2$. In the exceptional…
The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic group to a ramified cover. A version of Bertini Theorem in this context is also obtained.
Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in terms of a uniformly and absolutely convergent expansion. Term by term differentiation is possible with this expansion in the neighborhood of the surface. Methods for…
We consider a length functional for $C^1$ curves of fixed degree in graded manifolds equipped with a Riemannian metric. The first variation of this length functional can be computed only if the curve can be deformed in a suitable sense, and…
We prove the existence of an affine paving for the three-step flag Hilbert scheme $$ \text{Hilb}^{n, n+1, n+2}(0) := \left\{\mathbb{C}[[x,y]]\supset I_n\supset I_{n+1}\supset I_{n+2}: I_i \,\,\text{ ideals with } \text{dim}_{\mathbb{C}}…
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 construct five families of two-dimensional moduli spaces of parabolic Higgs bundles (respectively local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve. We…
A few formulas and theorems for statistical structures are proved. They deal with various curvatures as well as with metric properties of the cubic form or its covariant derivative. Some of them generalize formulas and theorems known in the…
The present paper shall provide a framework for working with Gr\"obner bases over arbitrary rings $k$ with a prescribed finite standard set $\Delta$. We show that the functor associating to a $k$-algebra $B$ the set of all reduced Gr\"obner…
We introduce the concept of the touching of two multifunctions on a real Hilbert space, and deduce that certain multifunctions on the space have a unique fixed point. These result are applied to the theory of genaralized cycles and…
We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the…
We calculate the cohomology spaces of the Hilbert schemes of points on surfaces with values in locally constant systems. For that purpose, we generalise I. Grojnoswki's and H. Nakajima's description of the ordinary cohomology in terms of a…
We study the closure of the locus of radical ideals in the multigraded Hilbert scheme associated with a standard graded polynomial ring and the Hilbert function of a homogeneous coordinate ring of points in general position in projective…