14029251.2014.975528.pdf (536.62 kB)
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
Published inJournal of Nonlinear Mathematical Physics
Pages543 - 583 (41)
CitationSCHREIBER, V. and VESELOV, A.P., 2014. On deformation and classification of V-Systems. Journal of Nonlinear Mathematical Physics, 21 (4), pp. 543 - 583.
PublisherCo-published by Atlantis Press and Taylor & Francis (© 2014 The Authors)
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/
NotesThis 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