Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves

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• 作者：M. Bertola (1) (2)
  A. Tovbis (3)
  
  1. Department of Mathematics and Statistics ; Concordia University ; 1455 de Maisonneuve W. ; Montreal ; QC ; Canada
  2. Centre recherches math茅matiques ; Universit茅 de Montr茅al ; C.聽P.聽6128 ; succ. centre ville ; Montreal ; QC ; Canada
  3. Department of Mathematics ; University of Central Florida ; 4000 Central Florida Blvd. ; Orlando ; FL ; 32816-1364 ; USA
  
• 关键词：Real and imaginary normalized differentials ; Degenerating Riemann surfaces ; Orthogonal polynomials
• 刊名：Analysis and Mathematical Physics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：5
• 期：1
• 页码：1-22
• 全文大小：343 KB
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  2. Krichever, I.M.: The averaging method for two-dimensional 鈥渋ntegrable鈥?equations. Anal. i Prilozhen. 22(3), 37鈥?2 (1988)
  3. Grushevsky, S., Krichever, I.: The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces. In: Surveys in Differential Geometry. Vol. XIV. Geometry of Riemann Surfaces and their Moduli Spaces, volume 14 of Surveys in Differential Geometry, pp. 111鈥?29. Int. Press, Somerville (2009)
  4. Bertola, M., Mo, M.Y.: Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights. Adv. Math. 220(1), 154鈥?18 (2009) CrossRef
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  11. Saff, E.B., Totik, V.: Logarithmic Potentials with External Fields, volume 316 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Berlin (1997) (Appendix B by Thomas Bloom)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1664-235X

文摘

We provide a direct and explicit proof that imaginary (real) normalized differentials of the second kind with prescribed polar part do not develop additional singularities as the underlying hyperelliptic Riemann surface degenerates in an arbitrary way.