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Autore: | Sabbah Claude |
Titolo: | Introduction to stokes structures / / Claude Sabbah |
Pubblicazione: | Berlin, : Springer, c2013 |
Edizione: | 1st ed. 2013. |
Descrizione fisica: | 1 online resource (XIV, 249 p. 14 illus., 1 illus. in color.) |
Disciplina: | 515/.354 |
Soggetto topico: | Differential equations, Linear |
Stokes' theorem | |
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. |
Titolo autorizzato: | Introduction to Stokes structures |
ISBN: | 3-642-31695-6 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910438153003321 |
Lo trovi qui: | Univ. Federico II |
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