The paper presents Colored Multiplanar Link Grammars (CMLG). These grammars are reducible to extended right-linear S-grammars (Wartena 2001) where the storage type S is a concatenation of c pushdowns. The number of colors available in these grammars induces a hierarchy of Classes of CMLGs. By fixing also another parameter in CMLGs, namely the bound t for non-projectivity depth, we get c-Colored...

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for the variety of characters of normalcrossing quasi-projective orbifold groups. Finally, we extend Sakuma’s formula for the first Betti number of abelian cove...

We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli R that can not be defined over R is also given.

We work on the classification of isomorphism classes finitely generated projective modules over C*-algebras $C\left( \mathbb{P}^{n}\left( \mathcal{T}\right) \right) $ and \mathbb{S}_{H}^{2n+1}\right) quantum complex spaces $\mathbb{P}^{n}\left( \mathcal{T} spheres $\mathbb{S}_{H}^{2n+1}$, line bundles $L_{k}$ $, studied by Hajac collaborators. Motivated groupoid approach Curto, Muhly, Renault t...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quas...