Related papers: On the birational geometry of matroids
In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions,…
This paper presents a bridge between the theories of wonderful models associated with toric arrangements and wonderful models associated with hyperplane arrangements. In a previous work, the same authors noticed that the model of the toric…
In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map.…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
In [19], the authors give minimal embedded toric resolutions of ADE-singularities in C^3 by constructing regular refinements of their dual Newton polyhedrons with the elements of their embedded valuation sets derived from the jet schemes…
The real intersection cohomology of a toric variety is described in a purely combinatorial way using methods of elementary commutative algebra only. We define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the fan as an…
Automorphisms of structural matrix algebras in block upper triangular form has been studied recently in \cite{Akkurt E-M Barker 2}, and this work is a follow-up paper of that study. The aim of this paper is to explain the topic in a much…
We construct a $\wedge$-homogeneous universal simple matroid of rank $3$, i.e. a countable simple rank~$3$ matroid $M_*$ which $\wedge$-embeds every finite simple rank $3$ matroid, and such that every isomorphism between finite…
In this paper we continue the study of good re-embeddings of affine K-algebras started in [KLR]. The idea is to use special linear projections to find isomorphisms between a given affine K-algebra K[X]/I, where X=(x_1,...,x_n), and…
We study the $C$- and $G$-patterns associated with rank $3$ skew-symmetrizable matrices of $B$-invariant type, including the Markov quiver. Motivated by the self-contained simple mutations in Markov-type cluster algebras, we prove that…
We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are geometric correspondences given by 3-manifolds realized in different ways as branched covers of the 3-sphere, up to branched cover…
In this paper, we begin by partitioning the edges (or arcs) of a circulant (di)graph according to which generator in the connection set leads to each edge. We then further refine the partition by subdividing any part that corresponds to an…
The {\em topological symmetry group} of an embedding $\Gamma$ of an abstract graph $\gamma$ in $S^3$ is the group of automorphisms of $\gamma$ which can be realized by homeomorphisms of the pair $(S^3, \Gamma)$. These groups are motivated…
We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers a question that appeared in an early version of the erratum of Birman and…
We determine explicit generators for the ring of modular forms associated with the moduli spaces of K3 surfaces with automorphism group $(\mathbb{Z}/2\mathbb{Z})^2$ and of Picard rank 13 and higher. The K3 surfaces in question carry a…
We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of $K3^{[n]}$ type is, in fact, induced by an automorphism of a $K3$ surface and the manifold is a moduli…
In this paper, we classify singular real plane tropical curves by means of subdivisions of Newton polytopes. First, we introduce signed Bergman fans (generalizing positive Bergman fans from [AKW06]) that describe real tropicalizations of…
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples…
We present a new type of equivalence for representable matroids that uses the automorphisms of the underlying matroid. Two $r\times n$ matrices $A$ and $A'$ representing the same matroid $M$ over a field $F$ are {\it geometrically…
A fan $F$ is \emph{endpoint-homogeneous} if for any two endpoints $e,e'$ of $F$, there is a homeomorphism $h: F \rightarrow F$ such that $h(e) = e'$. We prove there are uncountably many distinct homeomorphism types of endpoint-homogeneous…