Upper Bounds for Mutations of Potentials

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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dc.contributor.author	Cruz Morales, J.A.
dc.contributor.author	Galkin, S.
dc.date.accessioned	2019-02-19T18:44:11Z
dc.date.available	2019-02-19T18:44:11Z
dc.date.issued	2013
dc.identifier.citation	Upper Bounds for Mutations of Potentials / J.A. Cruz Morales, S. Galkin // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 13F60; 14J33; 53D37
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2013.005
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149210
dc.description.abstract	In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper bounds from [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52].	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Mirror Symmetry and Related Topics”. The full collection is available at http://www.emis.de/journals/SIGMA/mirror_symmetry.html. We want to thank Bernhard Keller for interesting discussions and in particular for suggesting the idea of considering upper bounds in the context of [9]. We thank Denis Auroux, Arkady Berenstein, Alexander Efimov, Alexander Goncharov and especially Alexandr Usnich for generously sharing their insights on mutations or mirror symmetry. We would like to thank Martin Guest for reading the draft of this paper and his valuable comments. We also want to thank the anonymous referees for their helpful comments and suggestions. First author was supported by a Japanese Government (Monbukagakusho:MEXT) Scholarship. Also this work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, Grant-in-Aid for Scientific Research (10554503) from Japan Society for Promotion of Science, Grant of Leading Scientific Schools (N.Sh. 4713.2010.1), grants ERC GEMIS and FWF P 24572- N25. The authors thank the IPMU for its hospitality and support during their visits in May and November 2012 which helped to finish this work.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Upper Bounds for Mutations of Potentials	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA