Compact complex surfaces

✍ Scribed by Barth W., Hulek K., Peters C., van de Ven A.

• Publisher: Springer
• Year: 2004
• Tongue: English
• Leaves: 444
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics
• Edition: 2ed
• Category: Library

✦ Synopsis

The first edition of "Compact Complex Surfaces" was published in 1984 and has become one of the most important books on the subject. In this second enlarged edition the major developments of the last 20 years have been incorporated. The Enriques-Kodaira classification is carried out in the spirit of Mori theory and many new developments have been added, including new analytic tools as well as new algebraic methods such as the theorems of Bogomolov and Reider and their applications. A new section is devoted to the stunning results achieved by the introduction of Donaldson and Seiberg-Witten invariants.

✦ Table of Contents

Table of Contents......Page all_4768_to_00437.cpc0006.djvu
Historical Note......Page all_4768_to_00437.cpc0010.djvu
The Contents of the Book......Page all_4768_to_00437.cpc0017.djvu
Standard Notation......Page all_4768_to_00437.cpc0021.djvu
1. Notation and Basic Pacts......Page all_4768_to_00437.cpc0022.djvu
2. Some Properties of Bilinear Forms......Page all_4768_to_00437.cpc0024.djvu
3. Vector Bundles, Characteristic Classes and the Index Theorem......Page all_4768_to_00437.cpc0030.djvu
4. Basic Concepts and Facts......Page all_4768_to_00437.cpc0032.djvu
5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch......Page all_4768_to_00437.cpc0033.djvu
6. Line Bundles and Divisors......Page all_4768_to_00437.cpc0035.djvu
7. Algebraic Dimension and Kodaira Dimension......Page all_4768_to_00437.cpc0037.djvu
8. Complex Spaces......Page all_4768_to_00437.cpc0039.djvu
9. The sigma-Process......Page all_4768_to_00437.cpc0043.djvu
10. Deformations of Complex Manifolds......Page all_4768_to_00437.cpc0044.djvu
11. De Rham Cohomology......Page all_4768_to_00437.cpc0048.djvu
12. Dolbeault Cohomology......Page all_4768_to_00437.cpc0050.djvu
13. Kähler Manifolds......Page all_4768_to_00437.cpc0051.djvu
14. Weight-1 Hodge Structures......Page all_4768_to_00437.cpc0057.djvu
15. Yau's Results on Kähler-Einstein Metrics......Page all_4768_to_00437.cpc0060.djvu
16. Ramification......Page all_4768_to_00437.cpc0062.djvu
17. Cyclic Coverings......Page all_4768_to_00437.cpc0063.djvu
18. Covering Tricks......Page all_4768_to_00437.cpc0064.djvu
19. GAGA Theorems and Projectivity Criteria......Page all_4768_to_00437.cpc0066.djvu
20. Theorems of Bertini and Lefschetz......Page all_4768_to_00437.cpc0067.djvu
1. Some Standard Exact Sequences......Page all_4768_to_00437.cpc0069.djvu
2. The Picard-Group of an Embedded Curve......Page all_4768_to_00437.cpc0071.djvu
3. Riemann-Roch for an Embedded Curve......Page all_4768_to_00437.cpc0073.djvu
4. The Residue Theorem......Page all_4768_to_00437.cpc0074.djvu
5. The Trace Map......Page all_4768_to_00437.cpc0076.djvu
6. Serre Duality on an Embedded Curve......Page all_4768_to_00437.cpc0078.djvu
7. The c-process......Page all_4768_to_00437.cpc0083.djvu
8. Simple Singularities of Curves......Page all_4768_to_00437.cpc0086.djvu
9. Intersection Multiplicities......Page all_4768_to_00437.cpc0089.djvu
10. Intersection Numbers......Page all_4768_to_00437.cpc0091.djvu
11. The Arithmetical Genus of an Embedded Curve......Page all_4768_to_00437.cpc0092.djvu
12. 1-Connected Divisors......Page all_4768_to_00437.cpc0093.djvu
1. Bimeromorphic Maps......Page all_4768_to_00437.cpc0096.djvu
2. Exceptional Curves......Page all_4768_to_00437.cpc0097.djvu
3. Rational Singularities......Page all_4768_to_00437.cpc0100.djvu
4. Exceptional Curves of the First Kind......Page all_4768_to_00437.cpc0104.djvu
5. Hirzebruch-Jung Singularities......Page all_4768_to_00437.cpc0106.djvu
6. Resolution of Surface Singularities......Page all_4768_to_00437.cpc0112.djvu
7. Singularities of Double Coverings, Simple Singularities of Surfaces......Page all_4768_to_00437.cpc0114.djvu
8. Generalities on Fibrations......Page all_4768_to_00437.cpc0117.djvu
9. The n-th Root Fibration......Page all_4768_to_00437.cpc0120.djvu
10. Stable Fibrations......Page all_4768_to_00437.cpc0121.djvu
11. Direct Image Sheaves......Page all_4768_to_00437.cpc0123.djvu
12. Relative Duality......Page all_4768_to_00437.cpc0125.djvu
13. Period Matrices of Stable Curves......Page all_4768_to_00437.cpc0128.djvu
14. Topological Monodromy of Stable Fibrations......Page all_4768_to_00437.cpc0129.djvu
15. Monodromy of the Period Matrix......Page all_4768_to_00437.cpc0132.djvu
16. Extending the Period Map......Page all_4768_to_00437.cpc0134.djvu
17. The Degree of f_* \omega_{X/S}......Page all_4768_to_00437.cpc0136.djvu
18. Iitaka's Conjecture C_{2,1}......Page all_4768_to_00437.cpc0138.djvu
1. Meromorphic Maps, Associated to Line Bundles......Page all_4768_to_00437.cpc0142.djvu
2. Hodge Theory on Surfaces......Page all_4768_to_00437.cpc0144.djvu
3. Existence of Kähler Metrics......Page all_4768_to_00437.cpc0151.djvu
4. Deformations of Surfaces......Page all_4768_to_00437.cpc0161.djvu
5. Some Inequalities for Hodge Numbers......Page all_4768_to_00437.cpc0164.djvu
6. Projectivity of Surfaces......Page all_4768_to_00437.cpc0166.djvu
7. The Nef Cone......Page all_4768_to_00437.cpc0169.djvu
8. Surfaces of Algebraic Dimension Zero......Page all_4768_to_00437.cpc0172.djvu
9. Almost-Complex Surfaces without any Complex Structure......Page all_4768_to_00437.cpc0173.djvu
10. Bogomolov's Theorem......Page all_4768_to_00437.cpc0175.djvu
11. Reider's Method......Page all_4768_to_00437.cpc0181.djvu
12. Vanishing Theorems on Surfaces......Page all_4768_to_00437.cpc0186.djvu
1. The Projective Plane P_2......Page all_4768_to_00437.cpc0192.djvu
2. Complete Intersections......Page all_4768_to_00437.cpc0194.djvu
3. Tori of Dimension 2......Page all_4768_to_00437.cpc0195.djvu
4. Ruled Surfaces......Page all_4768_to_00437.cpc0196.djvu
5. Elliptic Fibre Bundles......Page all_4768_to_00437.cpc0200.djvu
6. Higher Genus Fibre Bundles......Page all_4768_to_00437.cpc0206.djvu
7. Kodaira's Table of Singular Fibres......Page all_4768_to_00437.cpc0207.djvu
8. Stable Fibrations......Page all_4768_to_00437.cpc0209.djvu
9. The Jacobian Fibration......Page all_4768_to_00437.cpc0211.djvu
10. Stable Reduction......Page all_4768_to_00437.cpc0214.djvu
11. Classification......Page all_4768_to_00437.cpc0218.djvu
12. Invariants......Page all_4768_to_00437.cpc0219.djvu
13. Logarithmic Transformations......Page all_4768_to_00437.cpc0223.djvu
14. Kodaira Fibrations......Page all_4768_to_00437.cpc0227.djvu
15. The Godeaux Surface......Page all_4768_to_00437.cpc0230.djvu
17. Quotients of Products of Curves......Page all_4768_to_00437.cpc0231.djvu
18. Hopf Surfaces......Page all_4768_to_00437.cpc0232.djvu
19. Inoue Surfaces......Page all_4768_to_00437.cpc0234.djvu
20. Quotients of Bounded Domains in C^2......Page all_4768_to_00437.cpc0237.djvu
21. Hilbert Modular Surfaces......Page all_4768_to_00437.cpc0238.djvu
22. Invariants of Double Coverings......Page all_4768_to_00437.cpc0243.djvu
23. An Enriques Surface......Page all_4768_to_00437.cpc0245.djvu
24. Kummer Coverings......Page all_4768_to_00437.cpc0247.djvu
1. Statement of the Main Result......Page all_4768_to_00437.cpc0250.djvu
2. Characterising Minimal Surfaces whose Canonical Bundle is Nef......Page all_4768_to_00437.cpc0254.djvu
3. The Rationality Theorem and Castelnuovo's Criterion......Page all_4768_to_00437.cpc0255.djvu
4. The Case a(X) = 2......Page all_4768_to_00437.cpc0259.djvu
5. The Case a(X) = 1......Page all_4768_to_00437.cpc0262.djvu
6. The Case a(X) = 0......Page all_4768_to_00437.cpc0264.djvu
7. The Final Step......Page all_4768_to_00437.cpc0269.djvu
8. Deformations......Page all_4768_to_00437.cpc0270.djvu
1. Introduction......Page all_4768_to_00437.cpc0275.djvu
2. Some General Theorems......Page all_4768_to_00437.cpc0277.djvu
3. Noether's Inequality......Page all_4768_to_00437.cpc0279.djvu
4. The Inequality c_1^2 \le 3c_2......Page all_4768_to_00437.cpc0281.djvu
5. The Main Results......Page all_4768_to_00437.cpc0285.djvu
6. Proof of the Main Results......Page all_4768_to_00437.cpc0287.djvu
7. The Exceptional Cases and the 1-Canonical Map......Page all_4768_to_00437.cpc0292.djvu
Surfaces with Given Chern Numbers......Page all_4768_to_00437.cpc0296.djvu
8. The Geography of Chern Numbers......Page all_4768_to_00437.cpc0297.djvu
9. Surfaces on the Noether Lines......Page all_4768_to_00437.cpc0302.djvu
10. Surfaces with q = p_g = 0......Page all_4768_to_00437.cpc0305.djvu
1. Notation......Page all_4768_to_00437.cpc0312.djvu
2. The Results......Page all_4768_to_00437.cpc0314.djvu
3. Topological and Analytical Invariants......Page all_4768_to_00437.cpc0315.djvu
4. Digression on Affine Geometry over F_2......Page all_4768_to_00437.cpc0319.djvu
5. The Neron-Severi Lattice of Kummer Surfaces......Page all_4768_to_00437.cpc0321.djvu
6. The Torelli Theorem for Kummer Surfaces......Page all_4768_to_00437.cpc0327.djvu
7. The Local Torelli Theorem for K3-Surfaces......Page all_4768_to_00437.cpc0328.djvu
8. A Density Theorem......Page all_4768_to_00437.cpc0330.djvu
9. Behaviour of the Kähler Cone under Deformations......Page all_4768_to_00437.cpc0332.djvu
10. Degenerations of Isomorphisms between K3-Surfaces......Page all_4768_to_00437.cpc0334.djvu
11. The Torelli Theorems for K3-Surfaces......Page all_4768_to_00437.cpc0337.djvu
12. Construction of Moduli Spaces......Page all_4768_to_00437.cpc0339.djvu
13. Digression on Quaternionic Structures......Page all_4768_to_00437.cpc0341.djvu
14. Surjectivity of the Period Map......Page all_4768_to_00437.cpc0343.djvu
15. Topological and Analytic Invariants......Page all_4768_to_00437.cpc0344.djvu
16. Divisors on an Enriques Surface Y......Page all_4768_to_00437.cpc0345.djvu
17. Elliptic Pencils......Page all_4768_to_00437.cpc0347.djvu
18. Double Coverings of Quadrics......Page all_4768_to_00437.cpc0350.djvu
19. The Period Map......Page all_4768_to_00437.cpc0355.djvu
20. The Period Domain for Enriques Surfaces......Page all_4768_to_00437.cpc0357.djvu
21. Global Properties of the Period Map......Page all_4768_to_00437.cpc0359.djvu
22. Projective K3-surfaces and Mirror Symmetry......Page all_4768_to_00437.cpc0363.djvu
23. Special Curves on K3-Surfaces......Page all_4768_to_00437.cpc0369.djvu
24. An Application to Hyperbolic Geometry......Page all_4768_to_00437.cpc0374.djvu
1. Freedman's Results......Page all_4768_to_00437.cpc0379.djvu
2. Representability of Unimodular Forms......Page all_4768_to_00437.cpc0381.djvu
3. Introduction......Page all_4768_to_00437.cpc0383.djvu
4. The Donaldson Invariant, a Bird's Eye View......Page all_4768_to_00437.cpc0384.djvu
5. Infinitely many Homeomorphic Surfaces which are not Diffeomorphic......Page all_4768_to_00437.cpc0387.djvu
6. Further Results obtained by the Donaldson Method......Page all_4768_to_00437.cpc0394.djvu
7. Introduction......Page all_4768_to_00437.cpc0395.djvu
8. Properties of the Invariants......Page all_4768_to_00437.cpc0397.djvu
9. Surfaces Diffeomorphic to a Rational Surface......Page all_4768_to_00437.cpc0399.djvu
Bibliography......Page all_4768_to_00437.cpc0404.djvu
Notation......Page all_4768_to_00437.cpc0427.djvu
Index......Page all_4768_to_00437.cpc0430.djvu