Stefano Pasotti

Regular parallelisms in kinematic spaces

Here we propose a definition of regular parallelism in a linear space not necessarily embedded onto a projective space and we investigate its properties in the particular case of kinematic spaces. We prove that the kinematic parallelisms are always regular in that sense and we deduce some results on the group of translations acting transitively on the pointset.

Loops, regular permutation sets and graph colourings

Abstract We establish a correspondence among loops, regular permutation sets and directed graphs with a suitable edge colouring and relate some algebraic properties of the loop to configurations of the associated graph.

Holomorphic triples of genus 0

Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.

A construction of loops by means of regular permutation sets

Abstract Following the slid product construction for loops with inverses of [Pasotti, S. and E. Zizioli, Loops with two-sided inverses constructed by a class of regular permutation sets, J. Geom. 100 (2011), pp. 129–145. URL http://dx.doi.org/10.1007/s00022-011-0071-5 ], we present here the general setting ensuring the construction of a new loop ( L , ⊕ ) starting from loops ( K , + ) , ( P , + ˆ ) and ( P , + ) possessing suitable properties. The results established in the aforementioned note are generalized as well. Moreover we investigate the nuclei of L and the normality of subloops isomorphic to ( K , + ) and ( P , + ˆ ) .