Related papers: Describing Amoebas
In this short note we prove a lemma about the dimension of certain algebraic sets of matrices. This result is needed in our paper arXiv:1201.1672. The result presented here has also applications in other situations and so it should appear…
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
The volume of a line bundle is defined in terms of a limsup. It is a fundamental question whether this limsup is a limit. It has been shown that this is always the case on generically reduced schemes. We show that volumes are limits in two…
A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection…
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
Local and global amoebas are families of labeled graphs that satisfy interpolation properties on a fixed vertex set. A labeled graph $G$ on $n$ vertices is a local amoeba (resp. global amoeba) if there exists a sequence of feasible…
Given any complex Laurent polynomial $f$, $\mathrm{Amoeba}(f)$ is the image of its complex zero set under the coordinate-wise log absolute value map. We give an efficiently constructible polyhedral approximation, $\mathrm{ArchtTrop}(f)$, of…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…
Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…
The image of a holomorphic map germ is not necessarily locally open, and it is not always well-defined as a set germ. We find the structure of what becomes the image of a map germ when the target is a surface. We encode it as a decorated…
We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also…
A Hypercube $Q_n$ is a graph in which the vertices are all binary vectors of length n, and two vertices are adjacent if and only if their components differ in exactly one place. A galaxy or a star forest is a union of vertex disjoint stars.…
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…