Related papers: VersalDeformations - a package for computing versa…

In this paper, we will investigate the jet schemes of determinantal varieties. It is quite often the case that the geometric information concerning the jet schemes of an algebraic variety can be described, but the more refined algebraic…

We consider nilmanifolds with left-invariant complex structure and prove that small deformations of such structures are again left invariant if the Dolbeault-cohomology of the nilmanifold can be calculated using left-invariant forms. By a…

We develop methods for computing Hochschild cohomology groups and deformations of crossed product rings. We use these methods to find deformations of a ring associated to a particular orbifold with discrete torsion, and give a presentation…

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

We describe a method for computing discriminants for a large class of families of isolated determinantal singularities -- more precisely, for subfamilies of ${\mathcal G}$-versal families. The approach intrinsically provides a decomposition…

We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…

This short note provides a quick introduction to relative canonical resolutions of curves on rational normal scrolls. We present our Macaulay2-package which computes the relative canonical resolution associated to a curve and a pencil of…

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for cactus varieties of the third Veronese embedding.…

We discuss the geometric formulation of continuum defects consisting of dislocations and disclinations. After reviewing the metric affine geometry and the present geometric formulation of dislocation and disclination written in terms of…

Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…

We list all connected components of sets of non-discriminant functions near all {\em parabolic} function singularities (which are the second most important family of singularity classes of smooth functions after {\em simple} singularities).…

We introduce the AdditiveToricVarieties package for Macaulay2, a software system for algebraic geometry and commutative algebra, with methods for working with additive group actions on complete toric varieties. More precisely, we implement…

In this note we review the Singular library Inverse-syst.lib that implements Macaulay's correspondence and other related constructions for local rings.

This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction…

This note describes a package for computing seminormalization of rings within Macaulay2.

This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over…

The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the…

The signature of a path is a non-commutative power series whose coefficients are given by certain iterated integrals over the path coordinates. This series almost uniquely characterizes the path up to translation and reparameterization.…

We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…

\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…