SCHREIBER, V. and VESELOV, A.P., 2014. On deformation and classification of V-Systems. Journal of Nonlinear Mathematical Physics, 21 (4), pp. 543 - 583.
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.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence
(http://creativecommons.org/licenses/by/4.0/). It was published in the Journal of Nonlinear Mathematical Physics on 14 October 2014, available online: http://www.tandfonline.com/10.1080/14029251.2014.975528
The work of APV was partly supported by the EPSRC (grant EP/J00488X/1).