Integrable deformations and degenerations of some irregular singularities

DOI10.4171/PRIMS/57-3-2zbMath1487.34168arXiv1711.08514MaRDI QIDQ824246

Claude Sabbah

Publication date: 15 December 2021

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08514

zbMATH Keywords

isomonodromic deformationFrobenius manifoldirregular singularityBirkhoff problemformal decompositionreal blow-up

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items

The sixth Painlevé equation as isomonodromy deformation of an irregular system: monodromy data, coalescing eigenvalues, locally holomorphic transcendents and Frobenius manifolds, Riemann–Hilbert–Birkhoff inverse problem for semisimple flat F$F$‐manifolds and convergence of oriented associativity potentials, Moduli of Stokes torsors and singularities of differential equations, Isomonodromic Laplace transform with coalescing eigenvalues and confluence of Fuchsian singularities, Isomonodromic deformations along a stratum of the coalescence locus

Cites Work

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• Introduction to Stokes structures
• Asymptotic analysis for integrable connections with irregular singular points
• Good formal structures for flat meromorphic connections. I: Surfaces
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Differential equations with irregular singular points in dimension two
• Local moduli of semisimple Frobenius coalescent structures
• Isomonodromy deformations at an irregular singularity with coalescing eigenvalues
• Holonomic D-Modules with Betti Structures
• The Stokes Structure of a good meromorphic flat bundle
• Good formal structures for flat meromorphic connections, II: Excellent schemes
• Wild Harmonic Bundles and Wild Pure Twistor D-modules
• Good formal structure for meromorphic flat connections on smooth projective surfaces
• Analytic geometry of semisimple coalescent Frobenius structures
• Skeletons and moduli of Stokes torsors
• Results on the extension of isomonodromy deformations to the case of a resonant irregular singularity
• A remark on the irregularity complex