Introduction to Stokes Structures [[electronic resource] /] / by Claude Sabbah

• Record Nr.: UNISA996466480803316
• Autore: Sabbah Claude
• Pubbl/distr/stampa: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013
• ISBN: 3-642-31695-6
• Edizione: [1st ed. 2013.]
• Descrizione fisica: 1 online resource (XIV, 249 p. 14 illus., 1 illus. in color.)
• Collana: Lecture Notes in Mathematics, , 0075-8434 ; ; 2060
• Disciplina: 516.35
• Soggetti: Algebraic geometry; Differential equations; Approximation theory; Sequences (Mathematics); Functions of complex variables; Partial differential equations; Algebraic Geometry; Ordinary Differential Equations; Approximations and Expansions; Sequences, Series, Summability; Several Complex Variables and Analytic Spaces; Partial Differential Equations
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 1. T-filtrations -- ; 2. Stokes-filtered local systems in dimension one -- ; 3. Abelianity and strictness -- ; 4. Stokes-perverse sheaves on Riemann surfaces -- ; 5. The Riemann-Hilbert correspondence for holonomic D-modules on curves -- ; 6. Applications of the Riemann-Hilbert correspondence to holonomic distributions -- ; 7. Riemann-Hilbert and Laplace on the affine line (the regular case) -- ; 8. Real blow-up spaces and moderate de Rham complexes -- ; 9. Stokes-filtered local systems along a divisor with normal crossings -- ; 10. The Riemann-Hilbert correspondence for good meromorphic connections (case of a smooth divisor) -- ; 11. Good meromorphic connections ; (formal theory) -- ; 12. Good meromorphic connections (analytic theory) and the Riemann-Hilbert correspondence -- ; 13. Push-forward of Stokes-filtered local systems -- ; 14. Irregular nearby cycles -- ; 15. Nearby cycles of Stokes-filtered local systems.
• Sommario/riassunto: This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.