The Kobayashi-Hitchin Correspondence

3 avg rating
( 2 ratings by Goodreads )
 
9789810221683: The Kobayashi-Hitchin Correspondence
View all copies of this ISBN edition:
 
 

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 Kähler) case compared to the algebraic or Kähler 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.

"synopsis" may belong to another edition of this title.

Top Search Results from the AbeBooks Marketplace

1.

Martin Lubke, Andrei Teleman
Published by World Scientific Pub Co Inc (1995)
ISBN 10: 9810221681 ISBN 13: 9789810221683
New Hardcover Quantity Available: 1
Seller:
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating
[?]

Book Description World Scientific Pub Co Inc, 1995. Hardcover. Condition: New. Seller Inventory # DADAX9810221681

More information about this seller | Contact this seller

Buy New
US$ 71.33
Convert currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, rates & speeds

2.

Martin Lubke; Andrei Teleman
Published by World Scientific Pub Co Inc (1995)
ISBN 10: 9810221681 ISBN 13: 9789810221683
New Hardcover Quantity Available: 1
Seller:
Irish Booksellers
(Portland, ME, U.S.A.)
Rating
[?]

Book Description World Scientific Pub Co Inc, 1995. Condition: New. book. Seller Inventory # M9810221681

More information about this seller | Contact this seller

Buy New
US$ 94.65
Convert currency

Add to Basket

Shipping: US$ 3.27
Within U.S.A.
Destination, rates & speeds

3.

LUBKE
ISBN 10: 9810221681 ISBN 13: 9789810221683
New Quantity Available: 1
Seller:
University Bookstore
(DELHI, DELHI, India)
Rating
[?]

Book Description Condition: New. This is Brand NEW. Seller Inventory # Asian-15092018-4920

More information about this seller | Contact this seller

Buy New
US$ 118.43
Convert currency

Add to Basket

Shipping: US$ 10.60
From India to U.S.A.
Destination, rates & speeds