On deformation and classification of V-Systems
journal contributionposted on 2014-11-07, 09:09 authored by Veronika Schreiber, Alexander VeselovAlexander Veselov
The ∨-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of ∨-systems are known, but their classification is an open problem. We derive the relations describing the infinitesimal deformations of ∨-systems and use them to study the classification problem for ∨-systems in dimension three. We discuss also possible matroidal structures of ∨-systems in relation with projective geometry and give the catalogue of all known irreducible rank three ∨-systems.
The work of APV was partly supported by the EPSRC (grant EP/J00488X/1).
- Mathematical Sciences