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Sbornik: Mathematics, 2010, Volume 201, Issue 6, Pages 801–853
DOI: https://doi.org/10.1070/SM2010v201n06ABEH004093 (Mi sm7560) 		 
This article is cited in 6 scientific papers (total in 6 papers)

$\operatorname{SU}(2)$-monopoles, curves with symmetries and Ramanujan's heritage

H. W. Bradena, V. Z. Enolskib

a University of Edinburgh, UK
b Institute of Magnetism, National Academy of Sciences of Ukraine
English version PDF (681 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM2010v201n06ABEH004093
Abstract: We develop the Ercolani-Sinha construction of SU(2) monopoles for a five-parameter family of centred charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number-theoretic problem and a recently proven identity of Ramanujan provides a solution.
Bibliography: 36 titles.
Keywords: non-Abelian monopole, Ramanujan's hypergeometric identities, algebraic curves with automorphisms.
Received: 19.03.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 6, Pages 19–74
DOI: https://doi.org/10.4213/sm7560
Bibliographic databases:
Document Type: Article
UDC: 517.958:530.145.83+515.178.2+517.58
MSC: Primary 81T13, 14H70, 14H45; Secondary 14K25, 33Cxx
Language: English
Original paper language: Russian
Citation: H. W. Braden, V. Z. Enolski, “$\operatorname{SU}(2)$-monopoles, curves with symmetries and Ramanujan's heritage”, Mat. Sb., 201:6 (2010), 19–74; Sb. Math., 201:6 (2010), 801–853
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v201/i6/p19
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:240
    English version PDF:15
    References:78
    First page:19
     
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