Modern model theory can be viewed as a subject obsessed with notions of dimension, with the key examples furnished by linear dimension on the one hand, and the dimension of an algebraic variety (or, from another point of view, transcendences degree) on the other. There are several rigorous, and not always equivalent, notions of abstract dimension in use. For historical reasons the one we use is...

In his Ph.D. thesis, Cadegan-Schlieper constructs an invariant of the embedded topology a line arrangement which generalizes $$\mathcal {I}$$ -invariant introduced by Artal, Florens and author. This new is called loop-linking number in present paper. We refine result proving that homeomorphism type complement. give two effective methods to compute this invariant, both are based on braid monodro...

We study Zariski pairs of sextics which are distinguished by the Alexander polynomials. For this purpose, we present two constructive methods to produce explicit sextics of non-torus type with given configuration of simple singularities.