Upper Bounds for Mutations of Potentials
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....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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Інститут математики НАН України
2013
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| Zitieren: | 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. |
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Cruz Morales, J.A. Galkin, S. 2019-02-19T18:44:11Z 2019-02-19T18:44:11Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 13F60; 14J33; 53D37 DOI: http://dx.doi.org/10.3842/SIGMA.2013.005 https://nasplib.isofts.kiev.ua/handle/123456789/149210 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]. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Upper Bounds for Mutations of Potentials Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Upper Bounds for Mutations of Potentials |
| spellingShingle |
Upper Bounds for Mutations of Potentials Cruz Morales, J.A. Galkin, S. |
| title_short |
Upper Bounds for Mutations of Potentials |
| title_full |
Upper Bounds for Mutations of Potentials |
| title_fullStr |
Upper Bounds for Mutations of Potentials |
| title_full_unstemmed |
Upper Bounds for Mutations of Potentials |
| title_sort |
upper bounds for mutations of potentials |
| author |
Cruz Morales, J.A. Galkin, S. |
| author_facet |
Cruz Morales, J.A. Galkin, S. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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].
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149210 |
| citation_txt |
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. |
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AT cruzmoralesja upperboundsformutationsofpotentials AT galkins upperboundsformutationsofpotentials |
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2025-12-07T18:34:51Z |
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2025-12-07T18:34:51Z |
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1850875567489941504 |