Related papers: Computing epsilon multiplicities in graded algebra…
Let R be a standard graded ring over a commutative Noetherian ring with unity and I a graded ideal of R. Let M be a finitely generated graded R-module. We prove that there exist integers e and \rho_M(I) such that for all large n, reg(I^nM)=…
In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the…
A formula for the irregularity of abelian coverings of the projective plane is established and some applications are presented.
We consider multi-spike positive solutions to the Lane-Emden problem in any bounded smooth planar domain and compute their Morse index, extending to the dimension $N=2$ classical theorems due to Bahri-Li-Rey (1995) and Rey (1999) when…
Let $S=\mathbb{C}[x_{ij}]$ be a polynomial ring of $m\times n$ variables over $\mathbb{C}$ and let $I$ be the determinantal ideal of maximal minors of $S$. Using the representation theoretic techniques introduced in arXiv:1305.1719,…
The computational complexity of polynomial ideals and Gr\"obner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational…
We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, $\sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ...…
We use the theory of resolutions for a given Hilbert function to investigate the multiplicity conjectures of Huneke and Srinivasan and Herzog and Srinivasan. To prove the conjectures for all modules with a particular Hilbert function, we…
We undertake a detailed study of the sets of multiplicity in a second countable locally compact group $G$ and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space $\mathcal{B}(L^2(G))$…
We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise comparable, nonequivalent weight sequences admitting nonzero…
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate…
Exact tight bounds of the complexity of the satisfiability problem for dense modal logics is a difficult question, likely somewhere between $\PSPACE$ and $\EXPSPACE$ depending of the logic under question. For a class of them, called here…
We introduce a spectrum for arbitrary varieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for…
The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from…
We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural…
Fourier multiplier analysis is developed for nonlocal peridynamic-type Laplace operators, which are defined for scalar fields in $\mathbb{R}^n$. The Fourier multipliers are given through an integral representation. We show that the integral…
A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely…
Let $R$ be a Noetherian $\mathbb{N}$-graded ring. Let $L$, $M$ and $N$ be finitely generated graded $R$-modules with $N \subseteq M$. For a homogeneous ideal $I$, and for each fixed $k \in \mathbb{N}$, we show the asymptotic linearity of…
Multiplier ideals, and the vanishing theorems they satisfy, have found many applications in recent years. In the global setting they have been used to study pluricanonical and other linear series on a projective variety. More recently, they…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…