Isomonodromic deformations and Frobenius manifolds : an introduction
著者
書誌事項
Isomonodromic deformations and Frobenius manifolds : an introduction
（Universitext）
Springer , EDP Sciences, [2007]
- : Springer
- : EDP Sciences
- タイトル別名
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Déformations isomonodromiques et variétés de Frobenius
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注記
"Translation from the French language edition: Déformations isomonodromiques et variétés de Frobenius by Claude Sabbah. Copyright 2007 EDP Science, CNRS Editions, France."--T.p. verso
Includes bibliographical reference (p. [263]-271) and indexes
内容説明・目次
内容説明
Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
目次
The language of fibre bundles.- Holomorphic vector bundles on the Riemann sphere.- The Riemann-Hilbert correspondence on a Riemann surface.- Lattices.- The Riemann-Hilbert problem and Birkhoff's problem.- Fourier-Laplace duality.- Integrable deformations of bundles with connection on the Riemann sphere.- Saito structures and Frobenius structures on a complex analytic manifold.
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