  The V-systems are special finite sets of covectors which appeared in the
theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations.
Several families of V-systems are known but their classification is an open
problem. We derive the relations describing the infinitesimal deformations of
V-systems and use them to study the classification problem for V-systems in
dimension 3. We discuss also possible matroidal structures of V-systems in
relation with projective geometry and give the catalogue of all known
irreducible rank 3 V-systems.
