The canonical class and the C∞ properties of Kähler surfaces

New York Journal of Mathematics

Volumn 2, Issue , 1996, Pages 103-146

  Brussee, Rogier ^a  

^a BIELEFELD UNIVERSITY   (Germany)

Author keywords

dimensional intersection theory; 4 manifolds; Seiberg Witten theory; Surfaces

Indexed keywords

EID: 0001294652     PISSN: 10769803     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. [ACGH] E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of Algebraic Curves Grundlehren der Mathematischen Wissenschaften no. 276, Springer-Verlag, Berlin, 1985.
2. [Aub] T. Aubin, Nonlinear Analysis on Manifolds Monge-Ampère Equations. Grundlehren der Mathematischen Wissenschaften no. 252, Springer-Verlag, Berlin, 1982.
3. [BPV] W. Barth, C. Peters, and A. Van de Ven, Compact Complex Surfaces. Springer-Verlag, Berlin, 1984.
4. [BGV] N. Berline, E. Getzler, and M. Vergne, Heat Kernels and Dirac Operators. Springer-Verlag, Berlin, 1991.
5. [B1] S. Bradlow, Vortices in holomorphic line bundles over closed Kähler manifolds, Comm. Math. Phys. 135 (1990), 1-17.
6. [B2] S. Bradlow, Special metrics and stability for holomorphic bundles with global sections. J. Diff. Geom. 33 (1991), 169-214.
7. [Br1] R. Brussee, On the (-1) conjecture of Friedman and Morgan. Inv. Math. 114 (1993), 219-229.
8. [Br2] R. Brussee, Some remarks on the Kronheimer Mrowka classes of algebraic surfaces. J. Diff. Geom. 41 (1995), 269-275.
9. 2 Vanishing theorems for positive line bundles and adjunction theory. CIME lectures "Transcendental methods in algebraic geometry" Cetraro July 1994, preprint Inst. Fourier, alg-geom/9410022.
10. [Dol] Dold, A. Lectures on Algebraic Topology, Grundlehren der Mathematischen Wissenschaften no. 200, Springer-Verlag, Berlin, 1972.
11. [Don] S. K. D. Donaldson, Connections, cohomology and the intersection forms of four-manifolds. J. Differential Geometry 24 (1986), 275-341.
12. [FS1] R. Fintushel and R. Stern, Rational blowdown of smooth 4-manifolds, to appear in J. Diff. Geom, alg-geom/9505018.
13. [FS2] R. Fintushel and R. Stern, Immersed spheres in 4-manifolds and the immersed Thom conjecture, Turkish Journal of Mathematics 19 (1995), 145-157.
14. [FM1] R. Friedman and J. W. Morgan, Algebraic surfaces and 4-manifolds. Bull. A.M.S. 18 (1988), 1-19.
15. [FM2] R. Friedman and J. W. Morgan, Smooth Four Manifolds and Complex Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge Band 27, Springer-Verlag, Berlin, 1994.
16. [FM3] R. Friedman and J. W. Morgan, Algebraic surfaces and Seiberg-Witten invariants, alg-geom/9502026.
17. [FQ] R. Friedman and Z. Qin, On complex surfaces diffeomorphic to rational surfaces, alg-geom/9404010.
18. [Ful] W. Fulton, Intersection Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge Band 2, Springer-Verlag, Berlin, 1984.
19. [Gar] O. García-Prada, Invariant connections and vortices, Commun. Math. Phys. 156 (1993), 527-546.
20. [GT] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften no. 224, Springer-Verlag, Berlin, 1977.
21. [GM] M. Goresky and R. Mac Pherson, Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge Band 14, Springer-Verlag, Berlin, 1988.
22. [GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, John Wiley & Sons, New York, 1978.
23. [Kar] G. Karrer, Darstellung von Cliffordbündlen Ann. Acc. Sc. Fennicae, series A I. Mathematica, Helsinki 1973. (ISBN 951-41-0083-2)
24. [KW] J. Kazdan and F. W. Warner, Curvature functions for compact 2-manifolds. Ann. Math. 94 (1974), 14-47.
25. [Kob] S. Kobayashi, Differential Geometry of Complex Vector Bundles, Princeton Univ. Press, Princeton, 1987.
26. [Kot] D. Kotschick, On connected sum decompositions of algebraic surfaces and their fundamental groups, Internat. Math. Res. Notices (1993), 179-182.
27. [KM1] P. Kronheimer and T. Mrowka, Embedded surfaces and the structure of Donaldson's Polynomial invariants. J. Diff. Geom. 41 (1995), 573-734.
28. [KM2] P. Kronheimer and T. Mrowka, The Genus of embedded surfaces in the complex projective plane, preprint, 1994.
29. [OT1] C. Okonek and A. Teleman, Les invariants de Seiberg Witten et la conjecture de Van de Ven, Comptes Rendus (to appear), alg-geom/9505011.
30. [OT2] C. Okonek and A. Teleman, The coupled Seiberg Witten Equations, vortices, and the moduli spaces of stable pairs, alg-geom/9505012.
31. ∞ structures on algebraic surfaces, Encyclopedia of Mathematical Sciences no. 69, Several Complex Variables VI (complex manifolds), Springer-Verlag, Berlin, 1990, pp. 197-249.
32. [Pi1] V. Ya. Pidstrigatch, Deformation of instanton surfaces, Math. USSR Izv. 38 (1992), 313-331.
33. [Pi2] V. Ya. Pidstrigatch, Easy blow up formulas for Spin polynomials and a proof of the Van de Ven conjecture, Russian Acad. Sci. Izv. Math. (to appear). English translation alg-geom/9406007.
34. [P-T] V. Ya. Pidstrigatch and A. N. Tyurin, Invariants of the smooth structure of an algebraic surface arising from the Dirac operator, Russian Acad. Sci. Izv. Math. 40 (1993), 267-351.
35. [Spa] E. H. Spanier, Algebraic Topology, Wiley, 1966.
36. [Ste] R. Stern, talk at Stillwater OK, November, 1994.
37. [Ta1] C. Taubes, The Seiberg Witten invariants and symplectic forms, Math. Research Letters 1 (1994), 809-822.
38. [Ta2] C. Taubes, The Seiberg Witten and the Gromov invariants, Math. Research Letters 2 (1995), 221-238.
39. [VdV] A. Van de Ven, On the Differentiable Structure of Certain Algebraic Surfaces, Sém. Bourbaki no. 667, 1986.
40. [Wit] E. Witten, Monopoles and four manifolds. Math. Research letters 1 (1994), 769-796, preprint hep-th/9411102, IASSNS-HEP-94-96.