Related papers: Automorphism and Cohomology II: Complete intersect…

We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt…

We generalise the result of Tent and Ziegler to homogeneous structures that have a stationary independence relation without the symmetry axiom. We apply our result to prove simplicity of the automorphism group of some asymmetric examples…

We classify the pairs $(X,\pi)$, where $\pi\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational geometrically ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the…

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…

Let $X$ be a complex projective surface with arbitrary singularities. We construct a generalized Abel--Jacobi map $A_0(X)\to J^2(X)$ and show that it is an isomorphism on torsion subgroups. Here $A_0(X)$ is the appropriate Chow group of…

We construct automorphisms of $\C^n$ which map certain discrete sequences one onto another with prescribed finite jet at each point, thus solving a general Mittag-Leffler interpolation problem for automorphisms. Under certain circumstances,…

Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…

We show that all the automorphisms of the symmetric product Sym^d(X), d>2g-2, of a smooth projective curve X of genus g>2 are induced by automorphisms of X.

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.

Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_1,\dots,X_r$ the connected components of $X$. Assume that the integral cohomology of $X$ is torsion free and supported in even degrees. We prove that there exists a…

We observe that an interesting method to produce non-complete intersection subvarieties, the generalized complete intersections from L. Anderson and coworkers, can be understood and made explicit by using standard Cech cohomology machinery.…

If $X$ is a topological space then there is a natural homomorphism $\pi_1(X)\rightarrow K_1(X)$ from a fundamental group to a $K_1$-homology group. Covering projections depend of fundamental group. So $K_1$-homology groups are interrelated…

Let $A$ be a regular ring over a field $k$, with $1/2\in k$ and dimension $d$. We discuss the Homotopy Conjecture of Madhav V. Nori, in the complete intersection case (meaning when the projective module in question if free, of rank at least…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…

We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…

In this paper we shall prove that any $2$-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary…

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.