Scattered spaces in Galois geometry (Q2829806)

Let \(\Sigma = \mathrm{PG}(n-1,q)\), where \(t | n\). A \textit{scattered space} of \(\Sigma\) with respect to a \((t-1)\)-spread \({\mathcal S}\) of \(\Sigma\) is a subspace intersecting every spread element in at most a point. The concept of scattered space was first used by S. Ball and M. Lavrauw in order to construct an interesting \((q+1)\)-fold blocking set in \(\mathrm{PG}(2,q^4)\). Since then, scattered spaces turned out to be related to many other problems in Finite Geometry and therefore they have been and are currently investigated by many authors. The nice and useful survey under review is divided in two parts: the first part provides an overview of the known results regarding scattered spaces, while the second part is devoted to applications such as translation hyperovals, translation caps in affine spaces, linear sets, two-intersection sets, two-weight codes, blocking sets, embeddings of Segre varieties, pseudreguli, semifields, splashes of subgeometries and MRD-codes.NEWLINENEWLINEFor the entire collection see [Zbl 1345.11003].