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
Datum:2013
Hauptverfasser: Cruz Morales, J.A., Galkin, S.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2013
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/149210
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149210
record_format dspace
spelling 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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection 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].
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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first_indexed 2025-12-07T18:34:51Z
last_indexed 2025-12-07T18:34:51Z
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