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Catalogue Information
Field name	Details
Dewey Class	514.34
Title	Differential Topology of Complex Surfaces ([EBook]) : Elliptic Surfaces with p g =1: Smooth Classification / by John W. Morgan, Kieran G. O’Grady.
Author	Morgan, John W. , 1946-
Added Personal Name	O’Grady, Kieran G.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1993.
Physical Details	VII, 224 pages : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1545
ISBN	9783540476283
Summary Note	This book is about the smooth classification of a certain class of algebraicsurfaces, namely regular elliptic surfaces of geometric genus one, i.e. elliptic surfaces with b1 = 0 and b2+ = 3. The authors give a complete classification of these surfaces up to diffeomorphism. They achieve this result by partially computing one of Donalson's polynomial invariants. The computation is carried out using techniques from algebraic geometry. In these computations both thebasic facts about the Donaldson invariants and the relationship of the moduli space of ASD connections with the moduli space of stable bundles are assumed known. Some familiarity with the basic facts of the theory of moduliof sheaves and bundles on a surface is also assumed. This work gives a good and fairly comprehensive indication of how the methods of algebraic geometry can be used to compute Donaldson invariants.:
Contents note	Unstable polynomials of algebraic surfaces -- Identification of ?3,r (S, H) with ?3(S) -- Certain moduli spaces for bundles on elliptic surfaces with p g = 1 -- Representatives for classes in the image of the ?-map -- The blow-up formula -- The proof of Theorem 1.1.1.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0086765
Links to Related Works	Subject References: Algebraic Geometry . Complex manifolds . Differential Geometry . Manifolds and Cell Complexes (incl. Diff.Topology) . Manifolds (Mathematics) . Mathematics . Authors: author . Morgan, John W. 1946- . Morgan, John W., 1946- . O’Grady, Kieran G. . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 514.34 .

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Differential Topology of Complex Surfaces: Elliptic Surfaces with p g =1: Smooth Classification

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