Related papers: Normal Hilbert coefficients and elliptic ideals in…

The main message of the paper is that for Gorenstein singularities, whose (real) link is rational homology sphere, the Artin--Laufer program can be continued. Here we give the complete answer in the case of elliptic singularities. The main…

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of…

Let $\mathcal{H}_d^{(t)}$ ($t \geq -d$, $t>-3$) be the reproducing kernel Hilbert space on the unit ball $\mathbb{B}_d$ with kernel \[ k(z,w) = \frac{1}{(1-\langle z, w \rangle)^{d+t+1}} . \] We prove that if an ideal $I \triangleleft…

We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically,…

Let $\Sigma\subset \mathbb{R}^{2n}$ with $n\geq2$ be any $C^2$ compact convex hypersurface. The stability of closed characteristics has attracted considerable attention in related research fields. A long-standing conjecture states that all…

This paper studies mixed multiplicities of an arbitrary standard bigraded algebra and mixed multiplicities of two ideals I, J in a local ring (A,m), where I is an m-primary ideal and J an arbitrary ideal. The main results are criteria for…

Inner ideals of simple locally finite dimensional Lie algebras over an algebraically closed field of characteristic 0 are described. In particular, it is shown that a simple locally finite dimensional Lie algebra has a non-zero proper inner…

We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank two.

For a Noetherian local ring $(\RR, \m)$, the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an $\m$-primary ideal $I$ are known to code for properties of $\RR$, of the blowup of $\spec(\RR)$ along $V(I)$, and…

We extend the recent classification of Hilbert schemes with two Borel-fixed points to arbitrary characteristic. We accomplish this by synthesizing Reeves' algorithm for generating strongly stable ideals with the basic properties of…

In math.QA/0309252, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical)…

Let $(A,\frak m)$ be an excellent normal local ring with algebraically closed residue class field. Given integrally closed $\frak m$-primary ideals $I\supset J$, we show that there is a composition series between $I$ and $J$, by integrally…

We show that every integrally closed $\mathfrak{m}$-primary ideal $I$ in a commutative Noetherian local ring $(R,\mathfrak{m},k)$ has maximal complexity and curvature, i.e., $ {\rm cx}_R(I) = {\rm cx}_R(k) $ and $ {\rm curv}_R(I) = {\rm…

In this article we give an explicit formula for the jumping numbers of an ideal of finite colenght in a two-dimensional regular local ring with an algebraically closed residue field. For this purpose, we associate a certain numerical…

We consider the non-positivity of the Hilbert coefficients for a parameter ideal of a commutative Noetherian local ring. In particular, we show that the second Hilbert coefficient of a parameter ideal of depth at least d-1 is always…

This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The…

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…

This paper studies the jumping coefficients of principal ideals of regular local rings. Recently M. Blickle, M. Mustata and K. Smith showed that, when $R$ is of essentially finite type over a field and $F$-finite, bounded intervals contain…

We consider second-order partial differential operators $H$ in divergence form on $\Ri^d$ with a positive-semidefinite, symmetric, matrix $C$ of real $L_\infty$-coefficients and establish that $H$ is strongly elliptic if and only if the…

General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…