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# ðŸ“™ Geometric invariant theory and decorated principal bundles by Schmitt A.H.W. â€” free download

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The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal KobayashiHitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.

## About book:

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- Series:
**Zurich Lectures in Advanced Mathematics** - Author:
**Schmitt A.H.W.** - Year:
**2008** - Publisher:
**EMS** - Language:
**English** - ISBN:
**9783037190654,9783037190654**

- File size:
**3 572 378** - Format:
**pdf**

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Affine flag manifolds are infinite dimensional versions of familiar objects such as GraÃŸmann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significan...

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a mani...

This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable...

This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory. In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding ...

Greub W., Halperin S., Vanstone R. Connections, curvature, and cohomology. Vol.2.. Lie groups, principal bundles, and characteristic classes (AP, )(ISBN 0123027020)(543s)_MD_...

The canonical strategy of modern mathematics when studying an object is to put this object into a collection, and see what properties they have in common. Most commonly, the objects depend on some parameter(s), and the goal is to find out how the objects ...

Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. ...

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Launches of several major magnetospheric research satellites (i.e., Polar, Wind, and Interball) set the scene for extensive multi-platform investigations of the Earth's plasma environment in the era of the International Solar-Terrestrial Physics Program. ...

The book has no illustrations or index. Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Fiction / General; Religion / Hinduism / Sacred Writings;...

Magnetorheological fluids, smart fluids which change viscosity in the presence of a magnetic field, are of great commercial interest for many engineering applications such as shock absorbers and dampers in aerospace. Magnetorheology: Advances and Applicat...

THE MAGNIFICENT CENTURY, the second volume of Costain's A History of the Plantagenets, covers Henry III's long and turbulent reign, from 1216 to 1272. During his lifetime Henry was frequently unpopular, unreliable and inconsistent. Yet his reign saw spect...

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In 1908, when Gandhi was pioneering his passive resistance experiments inSouth Africa, Tolstoy wrote A Letter To A Hindu. A Letter To A Hindu was a reply toC.R. Das, a revolutionary representative of Indians in Europe, who had challengedTolstoyâ€™s philosop...