Related papers: Macaulay-like marked bases

We give a criterion for a collection of polynomials to be a universal Gr\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\mathbb{P}^1)^N$. This criterion can be used to give…

Let $G=H\ltimes K$ denote a semidirect product Lie group with Lie algebra $\mathfrak g=\mathfrak h \oplus \mathfrak k$, where $\mathfrak k$ is an ideal and $\mathfrak h$ is a subalgebra of the same dimension as $\mathfrak k$. There exist…

It is shown that the middle quasi-homomorphisms of Fujiwara and Kapovich are precisely constant perturbations of quasi-homomorphisms. Quasi-polynomial maps are defined and their constructibility is explored. In particular, it is shown that…

In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the…

We propose a general study of standard bases of polynomial ideals with parameters in the case where the monomial order is arbitrary. We give an application to the computation of the stratification by the local Hilbert-Samuel function.…

In this paper, we use elementary and simple ideas which are based on the significant applications of the power set ring to rebuild and study the patch topology on the prime spectrum from a completely different and new point of view.…

We describe the canonical module of a simplicial affine semigroup ring $\mathbb{K}[S]$ and its trace ideal. As a consequence, we characterize when $\mathbb{K}[S]$ is nearly Gorenstein in terms of arithmetic properties of the semigroup $S$.…

In recent years, there has been a considerable amount of interest in stability of equations and their corresponding groups. Here, we initiate the systematic study of the quantitative aspect of this theory. We develop a novel method,…

Let $\mathcal{X}$ be a tame proper Deligne-Mumford stack of the form $[M/G]$ where $M$ is a scheme and $G$ is an algebraic group. We prove that the stack $\mathcal{K}_{g,n}(\mathcal{X},d)$ of twisted stable maps is a quotient stack and can…

This paper studies stable sheaves on abelian surfaces of Picard number one. Our main tools are semi-homogeneous sheaves and Fourier-Mukai transforms. We introduce the notion of semi-homogeneous presentation and investigate the behavior of…

We say that an indecomposable Cartan matrix A with entries in the ground field of characteristic 0 is almost affine if the Lie sub(super)algebra determined by it is not finite dimensional or affine but the Lie (super)algebra determined by…

We prove that an $F$-crystal $(M,\vph)$ over an algebraically closed field $k$ of characteristic $p>0$ is determined by $(M,\vph)$ mod $p^n$, where $n\ge 1$ depends only on the rank of $M$ and on the greatest Hodge slope of $(M,\vph)$. We…

This paper is devoted to studying difference indices of quasi-prime difference algebraic systems. We define the quasi dimension polynomial of a quasi-prime difference algebraic system. Based on this, we give the definition of the difference…

The notion off-ideals is recent and has been studied in the papers[1] [2], [5], [10], [11], [12], [13], [14] and [15]. In this paper, we have generalized the idea off-ideals to quasi f-ideals. This extended class of ideals is much bigger…

It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…

We investigate the quotient ring $R$ of the ring of formal power series $\Q[[x_1,x_2,...]]$ over the closure of the ideal generated by non-constant quasi-\break symmetric functions. We show that a Hilbert basis of the quotient is naturally…

Let f:X-->Y be a semi-stable family of complex abelian varieties over a curve Y of genus q, and smooth over the complement of s points. If F(1,0) denotes the non-flat (1,0) part of the corresponding variation of Hodge structures, the…

Consider a family f:A --> U of g-dimensional abelian varieties over a quasiprojective manifold U. Suppose that the induced map from U to the moduli scheme of polarized abelian varieties is generically finite and that there is a projective…

The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system solving is also currently a bottleneck of index-calculus…

We investigate the structure and properties of symmetric ideals generated by general forms in the polynomial ring under the natural action of the symmetric group. This work significantly broadens the framework established in our earlier…