Related papers: Monomial resolutions of morphisms of algebraic sur…

Given an automorphism of a smooth complex algebraic curve, there is an induced action on the moduli space of semi-stable rank 2 holomorphic bundles with fixed determinant. We give a complete description of the fixed variety in terms of…

Given a birational map in the three dimensional projective space defined by monomials of degree $d$, we prove that its inverse is defined by monomials of degree at most $d^2-d+1$.

In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a flat structure, similar to geodesic laminations on hyperbolic surfaces. Here is a sequel to this article that aims at defining transversal measures on flat…

Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…

We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and morphisms of finite Tor-dimension, respectively. The class of…

We prove that the fixed ring of the $q$-division ring $k_q(x,y)$ under any finite group of monomial automorphisms is isomorphic to $k_q(x,y)$ for the same $q$. In a similar manner, we also show that this phenomenon extends to an…

We prove a result that relates the number of homomorphisms from the fundamental group of a compact nonorientable surface to a finite group $G$, where conjugacy classes of the boundary components of the surface must map to prescribed…

We show that endomorphisms of Weyl algebras over fields of characteristic zero are flat and that birational endomorphisms are automorphisms by reducing to positive characteristic. We also give examples showing that endomorphisms of Weyl…

The aim of this paper is sketch a theory of divisibility and factorisation in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely…

For any morphism of $\infty$-operads $\mathcal{P} \to \mathcal{O}$, we show that the free $\mathcal{O}$-algebra on a $\mathcal{P}$-algebra admits an explicit formula as the colimit over the $\mathcal{O}$-monoidal envelope of $\mathcal{P}$,…

Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…

Let $\varphi:F_1\to F_2$ be an injective morphism of free groups. If $\varphi$ is geometric (i.e. induced by an inclusion of oriented compact connected surfaces with nonempty boundary), then we show that $\varphi$ is an isometric embedding…

Given a map $\phi: X \to Y$ of $\mathbb Q$-factorial Mori dream spaces, one can ask whether this map is induced by a homogeneous homomorphism $R(Y) \to R(X)$ of Cox rings. As soon as $Y$ is singular, such a homomorphism needs not to exist,…

Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…

We discuss when a unital homomorphism {\phi} : C(X) \rightarrow A can be approximated by finite-dimensional homomorphisms, where X is a compact metric space and A is unital simple C*-algebra with tracial rank one. In this paper, we will…

In this paper we consider monomial localizations of monomial ideals and conjecture that a monomial ideal is polymatroidal if and only if all its monomial localizations have a linear resolution. The conjecture is proved for squarefree…

In this note we show that for a given irreducible binary quadratic form $f(x,y)$ with integer coefficients, whenever we have $f(x,y) = f(u,v)$ for integers $x,y,u,v$, there exists a rational automorphism of $f$ which sends $(x,y)$ to…

We study monodromy of holomorphic motions and show the equivalence of triviality of monodromy of holomorphic motions and extensions of holomorphic motions to continuous motions of the Riemann sphere. We also study liftings of holomorphic…

For a morphism $f : X \to Y$ of schemes, we give a tropical criterion for which points of $Y$ (valued in a field, discrete valuation ring, number ring, or Dedekind domain) lift to $X$. Our criterion extends the firmaments of Abramovich to a…

Homological smoothness and twisted Calabi-Yau property of generalized Weyl algebras over polynomial algebras in two variables is studied. A necessary and sufficient condition to be homologically smooth is given. The Nakayama automorphisms…