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Differential topology of complex surfaces : elliptic surfaces with pg̳=1: smooth classification

Author: John Morgan; Kieran G O'Grady; Millie Niss
Publisher: Berlin ; New York : Springer-Verlag, ©1993.
Series: Lecture notes in mathematics (Springer-Verlag), 1545.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book is about the smooth classification of a certainclass of algebraicsurfaces, namely regular ellipticsurfaces of geometric genus one, i.e. In these computationsboth thebasic facts about the  Read more...

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Additional Physical Format: Online version:
Morgan, John W., 1946-
Differential topology of complex surfaces.
Berlin ; New York : Springer-Verlag, ©1993
(OCoLC)625153729
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John Morgan; Kieran G O'Grady; Millie Niss
ISBN: 0387566740 9780387566740 3540566740 9783540566748
OCLC Number: 28112363
Description: 224 pages ; 24 cm.
Contents: 1. Introduction --
2. Unstable polynomials of algebraic surfaces --
2.2. A stratification of parameter spaces for vector bundles on [actual symbol not reproducible] --
2.3. The stratification of [actual symbol not reproducible] --
2.4. The [actual symbol not reproducible][subscript t] construction --
2.5. Analysis of the strata of [actual symbol not reproducible] --
2.6. Proofs of the theorems --
3. Identification of [actual symbol not reproducible] --
3.1. The main results --
3.2. The family of K3 surfaces with a section --
3.3. The family of minimal elliptic surfaces with multiple fibers --
3.4. The family of blown up elliptic surfaces --
3.5. Proof of Theorem 3.1.4 --
4. Certain moduli spaces for bundles on elliptic surfaces with p[subscript g] = 1 --
4.1. Background material on extensions of rank one sheaves --
4.2. The parameter spaces for properly semi-stable bundles --
4.3. The moduli spaces M[subscript c](S, H) for [actual symbol not reproducible] --
4.4. Irreducible components of [actual symbol not reproducible] associated to large divisors --
4.5. Four-dimensional components of M[subscript 2](S, H) --
4.6. Multiplicities --
4.7. Definition of [actual symbol not reproducible] --
5. Representatives for classes in the image of the v-map --
5.1. Representatives for the v map --
5.2. Passage from the blow-up to the original surface --
5.3. Enumerative Geometry --
5.4. [epsilon][subscript 2](S, H) --
6. The blow-up formula --
6.1. Outline of the proof of Theorem 6.0.1 for k = 2 --
6.2. First results --
6.3. An extension of the family [actual symbol not reproducible] --
6.4. Proof of Proposition 6.1.3 --
6.5. The contribution of the X[subscript i] --
6.6. The multiplicity of the X[subscript i] such that [actual symbol not reproducible] --
7. The proof of Theorem 1.1.1 --
7.1. Only the components of M[subscript 3](S, H) associated to large divisors contribute to the first two coefficients of [actual symbol not reproducible] --
7.2. The proof of the first part of Proposition 7.0.10 --
7.3. A further study of the components [actual symbol not reproducible] --
7.4. The computation of [actual symbol not reproducible] --
7.5. Proof of Formula (79) and of Proposition 7.0.12 --
8. Appendix: The non-simply connected case / John W. Morgan, Millie Niss and Kieran O'Grady --
8.1. Proof of Proposition 8.0.20 --
8.2. Proof of Proposition 8.0.21 --
8.3. Computation of [epsilon][subscript 2](S, H).
Series Title: Lecture notes in mathematics (Springer-Verlag), 1545.
Responsibility: John W. Morgan, Kieran G. O'Grady ; with the collaboration of Millie Niss.
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