@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 -
Kreußler, Bernd; Kurke, Herbert. Twistor spaces over the connected sum of 3 projective planes. Compositio Mathematica, Tome 82 (1992) no. 1, pp. 25-55. http://archive.numdam.org/item/CM_1992__82_1_25_0/
[AHS] Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond., Ser. A 362 (1978), 425-461. | MR | Zbl
, , :[BS] Méthodes Algébriques dans la Théorie Globale des Espaces Complexes I, II. Paris: Gauthier Villars, 1977. | Zbl
, :[Bes] Géométrie Riemannienne en Dimension 4. Paris: Cedic, 1981. | MR
:[BH] 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] First memoir on quartic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 19-69. | JFM
:[Cay2] Sketch of recent researches upon quartic and quintic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 186-195. | JFM
:[Cay3] Second memoir on quartic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 198-202. | JFM
:[Cay4] Third memoir on quartic surfaces. Proc. Lond. Math. Soc., I Ser. 3 (1871), 234-266. | JFM
:[Cle] Double solids. Adv. Math. 47 (1983), 107-230. | MR | Zbl
:[Dem] 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] Lectures on Algebraic Topology. Berlin, Heidelberg, New York: Springer-Verlag, 1972. | MR | Zbl
:[Don] An application of gauge theory to the topology of 4-manifolds. J. Differ. Geom. 18 (1983), 269-316. | MR | Zbl
:[DonF] Connected Sums of Self-Dual Manifolds and Deformations of Singular Spaces. Oxford, Mathematical Institute, 1988 (Preprint). | Zbl
, :[Floer] Selfdual Conformal Structures on 1CP 2 (Preprint 1987).
:[Free] The topology of four-dimensional manifolds. J. Differ. Geom. 17 (1982), 357-454. | MR | Zbl
:[Frie] 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] Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature. Math. Nachr. 106 (1982), 271-299. | MR | Zbl
, :[GH] Principles of Algebraic Geometry. New York: Wiley, 1978. | MR | Zbl
, :[Hir] Topological Methods in Algebraic Geometry. Berlin, Heidelberg, New York: Springer-Verlag, 1966. | MR | Zbl
:[HH] Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten. Math. Ann. 136 (1958), 156-172. | MR | Zbl
, :[Hit1] Linear field equations on self-dual spaces. Proc. R. Soc. Lond., Ser. A 370 (1980), 173-191. | MR | Zbl
:[Hit2] Kählerian twistor spaces. Proc. Lond. Math. Soc., III Ser. 43 (1981), 133-150. | MR | Zbl
:[Hur] The intersection of two quadrics in P 5(C) as a twistor space. Ann. Global Anal. Geom. 3 (1985), 185-195. | MR | Zbl
:[Jes] Quartic Surfaces. Cambridge: University Press, 1916. | JFM
:[Knut] Algebraic Spaces. Berlin, Heidelberg, New York: Springer-Verlag, 1971 (Lect. Notes Math. 203). | MR | Zbl
:[Kr] Small resolutions of double solids, branched over a 13-nodal quartic surface. Ann. Global Anal. Geom. 7 (1989), 227-267. | MR | Zbl
:[Kum] Über die Flächen vierten Grades mit sechzehn singulären Punkten. Monatsberichte der Königlichen PreuØischen Akademie der Wissenschaften zu Berlin (1864), 246-260.
:[K1] 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] Vorlesungen über algebraische Flächen. Leipzig: Teubner-Verlag, 1982 (Teubner-Texte zur Mathematik 43). | MR | Zbl
:[K3] Vanishing theorem for instanton bundles. To appear.
:[K4] A family of self-dual structures on the connected sum of projective planes. Preprint, Forschungsschwerpunkt komplexe Mannigfaltigkeiten, Nr. 60, Erlangen 1990.
:[Mil2] Singular Points of Complex Hypersurfaces. Princeton: University Press, 1968. | MR | Zbl
:[PTh] Compact Self-dual Manifolds with Positive Scalar Curvature. Oxford, St. Catherine's College, Thesis 1985. | MR | Zbl
:[Poon1] Compact self-dual manifolds with positive scalar curvature. J. Differ. Geom. 24 (1986), 97-132. | MR | Zbl
:[Poon2] Small Resolutions of Double Solids as Twistor Spaces (Preprint).
:[Poon3] Algebraic Dimension of Twistor Spaces. Math. Ann. 282 (1988), 621-627. | MR | Zbl
:[Sch] Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom. 20 (1984), 479-495. | MR | Zbl
:[Wer] Kleine Auftösungen spezieller dreidimensionaler Varietäten. Bonn, Max-Planck-Institut, 1987 (Preprint MPI 87-34). | MR
: