Related papers: Inverses of monomial Cremona maps
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…
We first introduce the class of quasi-algebraically stable meromorphic maps of $\P^k.$ This class is strictly larger than that of algebraically stable meromorphic self-maps of $\P^k.$ Then we prove that all maps in the new class enjoy a…
Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. We say that an oriented regular hypermap has \emph{duality-type} $\{l,n\}$…
A digraph $D$ is an oriented graph if $D$ does not have a pair of opposite arcs. The degree of a vertex $v$ of $D$ is the sum of the in-degree and out-degree of $v.$ Let $fvs(D)$ be the minimum number of vertices whose deletion from $D$…
Let X be a minimal complex surface of general type such that its image via the canonical map is a surface; we denote by d the degree of the canonical map. In this expository work, first of all we recall the known possibilities for the…
Let $D$ be a digraph on $p\geq 5$ vertices with minimum degree at least $p-1$ and with minimum semi-degree at least $p/2-1$. For $D$ (unless some extremal cases) we present a detailed proof of the following results [12]: (i) $D$ contains…
This is a sequel to the second and third author's Mixed Dimer Configuration Model in Type $D$ Cluster Algebras where we extend our model to work for quivers that contain oriented cycles. Namely, we extend a combinatorial model for…
This paper is a continuation of our previous works (see Mui\'c in Monatsh. Math. 180, no. 3, 607--629, (2016)) and (Mui\'c, Kodrnja in Ramanujan J. 55, no. 2, 393--420, (2021)) where we have studied maps from $X_0(N)$ into $\mathbb P^2$…
Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…
Explicit generators are found for the group of automorphisms of the algebra of one-sided inverses of a polynomial algebra in $n$ variables. An analogue of the polynomial Jacobian homomorphism is found.
The goal of this paper is the exact computation of the degrees $\text{deg}(f^n)$ of the iterates of birational maps $f: \mathbb{P}^N \dashrightarrow \mathbb{P}^N$. In the preceding companion paper, a new method has been proposed based on…
We derive a formula for the generating function of d-irreducible bipartite planar maps with several boundaries, i.e. having several marked faces of controlled degrees. It extends a formula due to Collet and Fusy for the case of arbitrary…
An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between $\Delta$-complexes is a $\Delta$-map that induces injections from star sets of $\mathcal D$ to star sets of $\mathcal C$. We study immersions between finite-dimensional…
We compute the multidegrees and the Segre numbers of general determinantal Cremona transformations, with generically reduced base scheme, by specializing to the standard Cremona transformation and computing its Segre class via mixed volumes…
Let $M\subset C^N$ be a minimal real-analytic CR-submanifold and $M'\subset C^{N'}$ a real-algebraic subset through points $p\in M$ and $p'\in M'$. We show that that any formal (holomorphic) mapping $f\colon (C^N,p)\to (C^{N'},p')$, sending…
The dual symmetric inverse monoid $\mathscr{I}_n^*$ is the inverse monoid of all isomorphisms between quotients of an $n$-set. We give a monoid presentation of $\mathscr{I}_n^*$ and, along the way, establish criteria for a monoid to be…
For a continuous map on a topological graph containing a unique loop S it is possible to define the degree and, for a map of degree 1, rotation numbers. It is known that the set of rotation numbers of points in S is a compact interval and…
Given two closed oriented manifolds $M,N$ of the same dimension, we denote the set of degrees of maps from $M$ to $N$ by $D(M,N)$. The set $D(M,N)$ always contains zero. We show the following (non-)realisability results: (i) There exists an…
The {\it inversion} of a set $X$ of vertices in a digraph $D$ consists in reversing the direction of all arcs of $D\langle X\rangle$. The {\it inversion number} of an oriented graph $D$, denoted by ${\rm inv}(D)$, is the minimum number of…
In this paper, we give a characterization of distance matrices of distance-regular graphs to be invertible.