Twistor spaces over the connected sum of 3 projective planes
Compositio Mathematica, Volume 82 (1992) no. 1, pp. 25-55.
@article{CM_1992__82_1_25_0,
     author = {Kreu{\ss}ler, Bernd and Kurke, Herbert},
     title = {Twistor spaces over the connected sum of 3 projective planes},
     journal = {Compositio Mathematica},
     pages = {25--55},
     publisher = {Kluwer Academic Publishers},
     volume = {82},
     number = {1},
     year = {1992},
     mrnumber = {1154160},
     zbl = {0766.53049},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1992__82_1_25_0/}
}
TY  - JOUR
AU  - Kreußler, Bernd
AU  - Kurke, Herbert
TI  - Twistor spaces over the connected sum of 3 projective planes
JO  - Compositio Mathematica
PY  - 1992
SP  - 25
EP  - 55
VL  - 82
IS  - 1
PB  - Kluwer Academic Publishers
UR  - http://archive.numdam.org/item/CM_1992__82_1_25_0/
LA  - en
ID  - CM_1992__82_1_25_0
ER  - 
%0 Journal Article
%A Kreußler, Bernd
%A Kurke, Herbert
%T Twistor spaces over the connected sum of 3 projective planes
%J Compositio Mathematica
%D 1992
%P 25-55
%V 82
%N 1
%I Kluwer Academic Publishers
%U http://archive.numdam.org/item/CM_1992__82_1_25_0/
%G en
%F CM_1992__82_1_25_0
Kreußler, Bernd; Kurke, Herbert. Twistor spaces over the connected sum of 3 projective planes. Compositio Mathematica, Volume 82 (1992) no. 1, pp. 25-55. http://archive.numdam.org/item/CM_1992__82_1_25_0/

[AHS] Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond., Ser. A 362 (1978), 425-461. | MR | Zbl

[BS] Bănică, C., Stănasilă, O.: Méthodes Algébriques dans la Théorie Globale des Espaces Complexes I, II. Paris: Gauthier Villars, 1977. | Zbl

[Bes] Besse, A.: Géométrie Riemannienne en Dimension 4. Paris: Cedic, 1981. | MR

[BH] Bombieri, E., Husemoller, D.: Classification and embeddings of surfaces. In: Algebraic Geometry, 1974. Providence, R.I., American Math. Soc. (1975), 329-420 (Proc. of Symp. Pure Math. 29). | MR | Zbl

[Cay1] Cayley, A.: First memoir on quartic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 19-69. | JFM

[Cay2] Cayley, A.: Sketch of recent researches upon quartic and quintic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 186-195. | JFM

[Cay3] Cayley, A.: Second memoir on quartic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 198-202. | JFM

[Cay4] Cayley, A.: Third memoir on quartic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 234-266. | JFM

[Cle] Clemens, H.: Double solids. Adv. Math. 47 (1983), 107-230. | MR | Zbl

[Dem] Demazure, M.: Surfaces de Del Pezzo II. V. In: Séminaire sur les Singularités des Surfaces. Berlin, Heidelberg, New York: Springer-Verlag, 1980 (Lect. Notes Math. 77). | Numdam | MR | Zbl

[Dold] Dold, A.: Lectures on Algebraic Topology. Berlin, Heidelberg, New York: Springer-Verlag, 1972. | MR | Zbl

[Don] Donaldson, S.K.: An application of gauge theory to the topology of 4-manifolds. J. Differ. Geom. 18 (1983), 269-316. | MR | Zbl

[DonF] Donaldson, S., Friedmann, R.: Connected Sums of Self-Dual Manifolds and Deformations of Singular Spaces. Oxford, Mathematical Institute, 1988 (Preprint). | Zbl

[Floer] Floer, A.: Selfdual Conformal Structures on 1CP 2 (Preprint 1987).

[Free] Freedman, M.: The topology of four-dimensional manifolds. J. Differ. Geom. 17 (1982), 357-454. | MR | Zbl

[Frie] Friedrich, Th.: Self-duality of Riemannian manifolds and connections. In: Self-dual Riemannian Geometry and Instantons. Leipzig: Teubner-Verlag, 1981 (Teubner-Texte zur Mathematik, 34). | MR

[FK] Friedrich, Th., Kurke, H.: Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature. Math. Nachr. 106 (1982), 271-299. | MR | Zbl

[GH] Griffiths, P., Harris, J.: Principles of Algebraic Geometry. New York: Wiley, 1978. | MR | Zbl

[Hir] Hirzebruch, F.: Topological Methods in Algebraic Geometry. Berlin, Heidelberg, New York: Springer-Verlag, 1966. | MR | Zbl

[HH] Hirzebruch, F., Hopf, H.: Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten. Math. Ann. 136 (1958), 156-172. | MR | Zbl

[Hit1] Hitchin, N.J.: Linear field equations on self-dual spaces. Proc. R. Soc. Lond., Ser. A 370 (1980), 173-191. | MR | Zbl

[Hit2] Hitchin, N.J.: Kählerian twistor spaces. Proc. Lond. Math. Soc., III Ser. 43 (1981), 133-150. | MR | Zbl

[Hur] Hurtubise, J.: The intersection of two quadrics in P 5(C) as a twistor space. Ann. Global Anal. Geom. 3 (1985), 185-195. | MR | Zbl

[Jes] Jessop, C.M.: Quartic Surfaces. Cambridge: University Press, 1916. | JFM

[Knut] Knutson, D.: Algebraic Spaces. Berlin, Heidelberg, New York: Springer-Verlag, 1971 (Lect. Notes Math. 203). | MR | Zbl

[Kr] Kreußler, B.: Small resolutions of double solids, branched over a 13-nodal quartic surface. Ann. Global Anal. Geom. 7 (1989), 227-267. | MR | Zbl

[Kum] Kummer, E.E.: Über die Flächen vierten Grades mit sechzehn singulären Punkten. Monatsberichte der Königlichen PreuØischen Akademie der Wissenschaften zu Berlin (1864), 246-260.

[K1] Kurke, H.: Applications of algebraic geometry to twistor spaces. In: Badescu, L., Kurke, H. (eds) Week of Algebraic Geometry) Leipzig: Teubner-Verlag, 1981 (Teubner-Texte zur Mathematik 40). | MR | Zbl

[K2] Kurke, H.: Vorlesungen über algebraische Flächen. Leipzig: Teubner-Verlag, 1982 (Teubner-Texte zur Mathematik 43). | MR | Zbl

[K3] Kurke, H.: Vanishing theorem for instanton bundles. To appear.

[K4] Kurke, H.: A family of self-dual structures on the connected sum of projective planes. Preprint, Forschungsschwerpunkt komplexe Mannigfaltigkeiten, Nr. 60, Erlangen 1990.

[Mil2] Milnor, J.: Singular Points of Complex Hypersurfaces. Princeton: University Press, 1968. | MR | Zbl

[PTh] Poon, Y.S.: Compact Self-dual Manifolds with Positive Scalar Curvature. Oxford, St. Catherine's College, Thesis 1985. | MR | Zbl

[Poon1] Poon, Y.S.: Compact self-dual manifolds with positive scalar curvature. J. Differ. Geom. 24 (1986), 97-132. | MR | Zbl

[Poon2] Poon, Y.S.: Small Resolutions of Double Solids as Twistor Spaces (Preprint).

[Poon3] Poon, Y.S.: Algebraic Dimension of Twistor Spaces. Math. Ann. 282 (1988), 621-627. | MR | Zbl

[Sch] Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom. 20 (1984), 479-495. | MR | Zbl

[Wer] Werner, J.: Kleine Auftösungen spezieller dreidimensionaler Varietäten. Bonn, Max-Planck-Institut, 1987 (Preprint MPI 87-34). | MR