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Upper Bounds for Mutations of Potentials
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- Фізико-технічні та математичні науки
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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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Upper Bounds for Mutations of Potentials
Інший ID:
2010 Mathematics Subject Classification: 13F60; 14J33; 53D37
DOI: http://dx.doi.org/10.3842/SIGMA.2013.005
DOI: http://dx.doi.org/10.3842/SIGMA.2013.005
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
553
Завантажень:
229
Анотація:
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].
