Table of Contents
Introduction iv
I. A brief survey of the structure and classification
of surfaces 1
Ruled surfaces 9
Elliptic surfaces 18
The classification table of surfaces 26
II. Thestructure of a degeneration 30
1. Thesingular fiber 30
2. The local behavior near the singular fiber 30
3. Theglobal structure of N close to tf 3 5
4. Intersection theory on N and itsapplications 37
5. The Mayer-Vietoris spectral sequence, and the
calculations of theBetti numbers of the general
fiber in terms of thespecial 50
6. Projective Degenerations 59
7. Mixed Hodge structures andthe Clemens-Schmid
exact sequence 61
III. Degenerations of surfaces 74
1. Specializations of birational isomorphisms and
some of its applications 75
2. Degenerations of elliptic surfaces 78
3. Degenerations of minimal
H
= 0 surfaces in the case
of no triple points 84
IV. Lemmas on Curves on Surfaces 101
V. Deformations of twosurfaces meeting along a
non-singular curve 112
1. C is rational 113
2. C is nonrational 119
Bibliography 123
Appendix
1. Elementary examples of degenerations 125
2. A degeneration of Enriques surfaces 131
3. A degeneration of Godeaux surfaces 134
4. The index of cruciality for elliptic curves in 139
elliptic ruled surfaces
Bibliography of the appendix 142
List of symbols and notational conventions
Index
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