We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action – the critical value of the Liouville action functional, considered as a function on the quasiFuchsian deformation space, is an antiderivative of a 1-form ...

let $mathcal{x}$ be a class of $r$-modules‎. ‎in this paper‎, ‎we investigate ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective (projective) complexes which are generalizations of injective (projective) and dg-injecti‎‎ve (projective) complexes‎. ‎we prove that some known results can be extended to the class of ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective ...

Using twisted and formal-local methods, we prove that every separated algebraic space which is the (open/flat) pushout of affine schemes has enough Azumaya algebras. As a corollary show that, under mild hypothesis, cohomological Brauer class representable by an algebra away from closed subset codimension $\geq 3$, generalizing early result Grothendieck. Next, $\mathrm{Br}(X)=\mathrm{Br}'(X)$ wh...

Purpose – In the literature, there is a lack of tools able to catch the symbolic dimension of the brand image, which go beyond rational and emotional dimensions. This paper aims to find and test a new instrument, named “Multi-Sensory Sort” (MuSeS). Design/methodology/approach – MuSeS, a direct methodology of exploring the consumer’s symbolic universe and the unconscious expectations, is compose...

 Let $R$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎A right $R$-module $M$ is called $(n‎, ‎d)$-projective if $Ext^{d+1}_R(M‎, ‎A)=0$ for every $n$-copresented right $R$-module $A$‎. ‎$R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $R$-module is $(n‎, ‎d)$-projective‎. ‎$R$...

We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the a...

Let P (S) denote the space of projective structures on a closed surface S. It is known that the subset Q(S) P (S) of projective structures with quasiFuchsian holonomy has in nitely many connected components. In this paper, we investigate the con guration of these components. In particular, we show that the closure of any exotic component of Q(S) intersects the closure of the standard component ...

Throughout this paper, we fix an algebraically closed field k. Let f : X → Y be a surjective and projective morphism of quasi-projective varieties over k with dim f = 1. Let E be a vector bundle of rank r on X . Then, we define the discriminant divisor of E with respect to f : X → Y to be disX/Y (E) = f∗ (( 2rc2(E)− (r − 1)c1(E) ) ∩ [X ]) . Here f∗ is the push-forward of cycles, so that disX/Y ...

In this paper, we prove a generalization of Reznikov's theorem on the torsion-property of the Chern-Simons classes and in particular the torsion–property of the Deligne Chern classes (in degrees > 1) of a flat vector bundle on a smooth complex projective variety. We consider the case of a smooth quasi–projective variety with an ir-reducible smooth divisor at infinity. We define the Chern-Simons...