menu

The Kobayashi-Hitchin Correspondence
by Martin Lubke and Andrei Teleman




Overview -
By the Kobayashi-Hitchin correspondence, the authors of this book mean the isomorphy of the moduli spaces Mst of stable holomorphic -- resp. MHE of irreducible Hermitian-Einstein -- structures in a differentiable complex vector bundle on a compact complex manifold. They give a complete proof of this result in the most general setting, and treat several applications and some new examples.After discussing the stability concept on arbitrary compact complex manifolds in Chapter 1, the authors consider, in Chapter 2, Hermitian-Einstein structures and prove the stability of irreducible Hermitian-Einstein bundles. This implies the existence of a natural map I from MHE to Mst which is bijective by the result of (the rather technical) Chapter 3. In Chapter 4 the moduli spaces involved are studied in detail, in particular it is shown that their natural analytic structures are isomorphic via I. Also a comparison theorem for moduli spaces of instantons resp. stable bundles is proved; this is the form in which the Kobayashi-Hitchin has been used in Donaldson theory to study differentiable structures of complex surfaces. The fact that I is an isomorphism of real analytic spaces is applied in Chapter 5 to show the openness of the stability condition and the existence of a natural Hermitian metric in the moduli space, and to study, at least in some cases, the dependence of Mst on the base metric used to define stability. Another application is a rather simple proof of Bogomolov's theorem on surfaces of type VII0. In Chapter 6, some moduli spaces of stable bundles are calculated to illustrate what can happen in the general (i.e. not necessarily K hler) case compared to the algebraic or K hler one. Finally, appendices containing results, especially from Hermitian geometry and analysis, in the form they are used in the main part of the book are included.

  Read Full Product Description
 
local_shippingFor Delivery
On Order. Usually ships in 2-4 weeks
This item is Non-Returnable.
FREE Shipping for Club Members help
 
storeBuy Online Pickup At Store
search store by zipcode

 
 
New & Used Marketplace 3 copies from $132.93
 
 
 

More About The Kobayashi-Hitchin Correspondence by Martin Lubke; Andrei Teleman

 
 
 

Overview

By the Kobayashi-Hitchin correspondence, the authors of this book mean the isomorphy of the moduli spaces Mst of stable holomorphic -- resp. MHE of irreducible Hermitian-Einstein -- structures in a differentiable complex vector bundle on a compact complex manifold. They give a complete proof of this result in the most general setting, and treat several applications and some new examples.After discussing the stability concept on arbitrary compact complex manifolds in Chapter 1, the authors consider, in Chapter 2, Hermitian-Einstein structures and prove the stability of irreducible Hermitian-Einstein bundles. This implies the existence of a natural map I from MHE to Mst which is bijective by the result of (the rather technical) Chapter 3. In Chapter 4 the moduli spaces involved are studied in detail, in particular it is shown that their natural analytic structures are isomorphic via I. Also a comparison theorem for moduli spaces of instantons resp. stable bundles is proved; this is the form in which the Kobayashi-Hitchin has been used in Donaldson theory to study differentiable structures of complex surfaces. The fact that I is an isomorphism of real analytic spaces is applied in Chapter 5 to show the openness of the stability condition and the existence of a natural Hermitian metric in the moduli space, and to study, at least in some cases, the dependence of Mst on the base metric used to define stability. Another application is a rather simple proof of Bogomolov's theorem on surfaces of type VII0. In Chapter 6, some moduli spaces of stable bundles are calculated to illustrate what can happen in the general (i.e. not necessarily K hler) case compared to the algebraic or K hler one. Finally, appendices containing results, especially from Hermitian geometry and analysis, in the form they are used in the main part of the book are included.


This item is Non-Returnable.

 

Details

  • ISBN-13: 9789810221683
  • ISBN-10: 9810221681
  • Publisher: World Scientific Publishing Company
  • Publish Date: September 1995
  • Page Count: 264
  • Dimensions: 8.6 x 6.2 x 0.9 inches
  • Shipping Weight: 1.15 pounds


Related Categories

 

BAM Customer Reviews