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Titlebook: Introduction to Stokes Structures; Claude Sabbah Book 2013 Springer-Verlag Berlin Heidelberg 2013 34M40, 32C38, 35A27.Meromorphic connecti

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發(fā)表于 2025-3-21 19:24:03 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Introduction to Stokes Structures
編輯Claude Sabbah
視頻videohttp://file.papertrans.cn/475/474236/474236.mp4
概述A first part on the classical theory of linear differential equations in the complex domain revisited from a geometric view point..Original and new study of the Stokes phenomenon in higher dimension..
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: Introduction to Stokes Structures;  Claude Sabbah Book 2013 Springer-Verlag Berlin Heidelberg 2013 34M40, 32C38, 35A27.Meromorphic connecti
描述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.
出版日期Book 2013
關(guān)鍵詞34M40, 32C38, 35A27; Meromorphic connection; Stokes filtration; Stokes-perverse sheaf; real blowing-up; o
版次1
doihttps://doi.org/10.1007/978-3-642-31695-1
isbn_softcover978-3-642-31694-4
isbn_ebook978-3-642-31695-1Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2013
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沙發(fā)
發(fā)表于 2025-3-21 20:47:40 | 只看該作者
板凳
發(fā)表于 2025-3-22 01:55:59 | 只看該作者
The Riemann–Hilbert Correspondence for Holonomic ,-Modules on Curvesperverse sheaves. It is induced from a functor at the derived category level which is compatible with .-structures. Given a discrete set . in ., we first define the functor from the category of .-modules which are holonomic and have regular singularities away from . to that of Stokes-perverse sheave
地板
發(fā)表于 2025-3-22 06:01:51 | 只看該作者
Applications of the Riemann–Hilbert Correspondence to Holonomic Distributionsis also holonomic. As an application, we make explicit the local expression of a holonomic distribution, that is, a distribution on . (in Schwartz’ sense) which is solution to a nonzero holomorphic differential equation on .. The conclusion is that working with . objects hides the Stokes phenomenon.
5#
發(fā)表于 2025-3-22 10:26:20 | 只看該作者
Riemann–Hilbert and Laplace on the Affine Line (the Regular Case). provides the simplest example of an irregular singularity (at infinity). We will describe the Stokes-filtered local system attached to . at infinity in terms of data of .. More precisely, we define the topological Laplace transform of the perverse sheaf . as a perverse sheaf on . equipped with a S
6#
發(fā)表于 2025-3-22 14:49:41 | 只看該作者
Real Blow-Up Spaces and Moderate de Rham Complexes is defined the sheaf of holomorphic functions with moderate growth, whose basic properties are analyzed. The moderate de Rham complex of a meromorphic connection is introduced, and its behaviour under the direct image by a proper modification is explained. This chapter ends with an example of a mod
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發(fā)表于 2025-3-22 18:24:55 | 只看該作者
8#
發(fā)表于 2025-3-22 21:55:34 | 只看該作者
The Riemann–Hilbert Correspondence for Good Meromorphic Connections (Case of a Smooth Divisor)t to the parameters. This is the meaning of the goodness condition in the present setting. We will have to treat the Riemann–Hilbert functor in a more invariant way, and more arguments will be needed in the proof of the main result (equivalence of categories) in order to make it global with respect
9#
發(fā)表于 2025-3-23 01:30:37 | 只看該作者
10#
發(fā)表于 2025-3-23 05:56:01 | 只看該作者
Irregular Nearby Cyclesbraic case. We give a new proof of this theorem when the support of the holonomic .-module has dimension two, which holds in the complex analytic setting and which makes more precise the non-vanishing nearby cycles.
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