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On deformation and classification of V-Systems

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journal contribution
posted on 07.11.2014, 09:09 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.

Funding

The work of APV was partly supported by the EPSRC (grant EP/J00488X/1).

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Nonlinear Mathematical Physics

Volume

21

Issue

4

Pages

543 - 583 (41)

Citation

SCHREIBER, V. and VESELOV, A.P., 2014. On deformation and classification of V-Systems. Journal of Nonlinear Mathematical Physics, 21 (4), pp. 543 - 583.

Publisher

Co-published by Atlantis Press and Taylor & Francis (© 2014 The Authors)

Version

AM (Accepted Manuscript)

Publisher statement

This 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/

Publication date

2014

Notes

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

ISSN

1402-9251

Language

en

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