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References
Artin, M., "On the solutions of analytic equations," Invent. Math., 5 (1968), 277–291, MR 38 #344.
Artin, M., "Algebraization of formal moduli, I, Global Analysis," Princeton Univ. Press, Princeton, N.J., and Tokyo Univ. Press, Tokyo, 1969, 21–71, MR 41#5369.
Atiyah, M. I., Singer, I. M., "The index of elliptic operators III," Ann. Math., 87 (1968), 546–604.
Bagnera, G., De Franchis, M., "Sopra le superficie algebriche che hanno le coordinate del punto generico esprimibili con funzioni meromorfe quadruplemente periodiche di 2 parametri," Rend. Acc. dei Lincei 16 (1907).
Barth, W., Peters, C., van de Ven, A., "Compact complex surfaces," Springer Ergebnisse 4, (1984), Berlin-Heidelberg.
Beauville, A., "Surfaces algébriques complexes," Astérisque, 54 (1978).
Bombieri, E., "Canonical models of surfaces of general type," Publ. Scient. I.H.E.S. 42 (1973), 447–495.
Bombieri, E., Husemoller, D., "Classification and embeddings of surfaces," in Algebraic Geometry, Arcata 1974, A.M.S. Proc. Symp. Pure Math., 29 (1975), 329–420.
Borcea, C., "Some remarks on deformations of Hopf manifolds, Rev. Roum. Math. Pures Appl., 26 (1981), 1287–1294.
Barns, D., Wahl, J., "Local contributions to global deformations of surfaces," Inv. Math., 26 (1974), 67–88.
Castelnuovo, G., "Sul numero dei moduli di una superficie irregolare, I, II," Rend. Accad. Lincei, 7 (1949), 3–7, 8–11.
Catanese, F., "Moduli of surfaces of general type," in Algebraic Geometry-Open problems, Proc. Ravello 1982, Springer L.N.M. 997 (1983), 90–112.
Catanese, F., "Superficie complesse compatte," Atti Convegno G.N.S.A.G.A. del C.N.R., Valetto, Torino (1986)
Catanese, F., "Canonical rings and "special" surfaces of general type," Proc. of A.M.S. Conf. in Algebraic Geometry, 1985.
Catanese, F., "Commutative algebra methods and equations of regular surfaces," in Alg. Geometry-Bucharest 1982, Springer L.N.M. 1056 (1984), 68–111.
Catanese, F., "On the period map of surfaces with K2=x=2," in Classification of Algebraic and Analytic Manifolds, Proc. Katata Symp. 1982, P.M. 33 Birkhäuser (1983), 27–43.
Catanese, F., "On the moduli spaces of surfaces of general type," J. Diff. Geom., 19 (1984), 483–515.
Catanese, F., "Automorphisms of rational double points and moduli spaces of surfaces of general type," Comp. Math. 61 (1987) 81–102.
Catanese, F., "Connected components of moduli spaces," J. Diff. Geom. 24 (1986) 395–399.
Ciliberto, C., "Superficie algebriche complesse: idee e metodi della classificazione" in Atti del Convegno di Geometria Algebrica, Nervi 1984, Tecnoprint Bologna (1984), 39–157.
Ciliberto, C., "Sul grado dei generatori dell'a nello canonico di una superficie di tipo generale," Rend. Sem. Mat. Univ. e Polit. di Torino 41, 3 (1983), 83–112.
Dabrowski, K., "Moduli spaces for Hopf surfaces," Math. Ann., 259 (1982), 201–226.
Donaldson, S., "An application of gauge theory to four dimensional topology," J. Diff. Geom., 18 (1983), 279–315.
Donaldson, S., "La topologie differentielle des surfaces complexes," C.R. Acad. Sc. Paris 301, I, 6 (1985), 317–320.
Douady, A., "Le probleme des modules pour les variétés analytiques complexes, Sém. Bourbaki (1964/65), exposé 277.
Douady, A., "Flatness and privilege," in Topics in several complex variables, Monographie n. 17 de l'Ens. Math., Geneve (1968), 47–74.
Douady, A., "Obstruction primaire à la dèformation, Séminaire H. Cartan, 13c Annee (1960/61), exposé 4.
Douady, A., "Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné," Ann. Inst. Fourier (Grenoble) 16 (1966), fasc. 1, 1–95, MR 34 #2940.
Ehresmann, C., ""Sur les espaces fibrés différentiables," C. R. Acad. Sci. Paris, 224 (1947), 1611–1612.
Enriques, F., "Le superficie algebriche," Zanichelli, Bologna (1949)
Forster, O., "Power series methods in deformation theory," Proc. Symp. Pure Math., 30 (1977), A.M.S., 199–217.
Francia, P., "The bicanonical map for surfaces of general type," to appear in Math. Ann.
Freedman, M. H., "The topology of four dimensional manifolds," J. Diff. Geom., 17 (1982), 357–453.
Gieseker, D., "Global moduli for surfaces of general type," Inv. Math. 43 (1977), 233–282.
Grauert, H., "Über die Deformation isolierter Singularitäten analytischer Mengen," Invent. Math., 15 (1972), 171–182, MR 45 #2206.
Grauert, H., "Über Modifikationen und exzeptionelle analytische Mengen," Math. Ann., 146 (1962), 331–368.
Grauert, H., "Der Satz von Kuranishi für kompakte komplexe Raüme, Invent. Math., 25 (1974), 107–142, MR 49 #10920.
Griffiths, Ph. A., "Periods of integrals on algebraic manifolds, I. II," Amer. J. Math., 90 (1968), 568–626, 805–865, MR 37 #5215, 38 #2146.
Griffiths, P., Harris, J, "Infinitesimal variation of Hodge structure II," Comp. Math 50 (1983), 207–265.
Grothendieck, A., "Construction de l'espace de Teichmùller, Séminaire H. Cartan, 13c Année (1960/61), Exposé 17.
Grothendieck, A., "Techniques de construction II; Le théorème d' existence en théorie formelle des modules, Sém. Bourbaki, exp. 195 Scre. Math. Paris (1960); Techniques de construction IV: Les schémas de Hilbert, Sém. Bourbaki, exp. 221, Secr. Math. Paris (1961).
Habegger, N., "Une variété de dimension 4 avec forme d'intersection paire et signature-8," Comm. Math. Helv., 57 (1982), 22–24.
Harris, J., Mumford, D., "On the Kodaira dimension of the moduli space of curves," Invent. Math., 67 (1982), 23–86.
Hicks, N., "Notes on differential geometry," Van Nostrand, New York (1965).
Hirzebruch, F., "Topological methods in algebraic geometry, Springer-Verlag, Grundlehren 131, 3rd ed. (1966).
Horikawa, E., "On deformations of holomorphic maps," in Manifolds-Tokyo 1973, Iwanami-Shoten (1974), 383–388.
Horikawa, E., "On deformations of holomorphic maps I," J. Math. Soc. Japan, 25 (1973), 372–396.
Horikawa, E., "On deformations of holomorphic maps II," J. Math. Soc. Japan 26, 647–667, III ibidem.
Horikawa, E., "On deformations of quintic surfaces," Inv. Math., 31 (1975), 43–85.
Horikawa, E., "On the number of moduli of certain algebraic surfaces of general type," J. Fac. Sci. Univ. Tokyo (1974), 67–78.
Hörmander, L., "An introduction to complex analysis in several variables," II ed., North Holland, Amsterdam (1973).
Kas, A., "On obstructions to deformations of complex analytic surfaces," Proc. Nat. Acad. Sci. U.S.A., 58 (1967), 402–404.
Kodaira, K., "On stability of compact submanifolds of complex manifolds," Amer. J. Math., 85 (1963), 79–94, MR 27 #3002.
Kodaira, K., "A theorem of completeness for analytic systems of surfaces, with ordinary singularities," Ann. Math., 74 (1961), 591–627.
Kodaira, K., "On characteristic systems of families of surfaces with ordinary singularities in a projective space," Amer. J. Math., 87 (1965), 227–256.
Kodaira, K., "On the structure of compact complex analytic surfaces, I," Amer. J. Math., 86 (1964), 751–798.
Kodaira, K., Morrow, J., "Complex manifolds," Holt, Rinehart and Winston, New York (1971).
Kodaira, K., Nirenberg, L., Spencer, D. C., "On the existence of deformations of complex analytic structures," Ann. Math. (2) 68, (1958), 450–459, MR 22 #3012.
Kodaira, K., Spencer, D. C., "On deformations of complex analytic structures, I, II," Ann. Math. (2) 67 (1958), 328–466, MR 22 #3009.
Kodaira, K., Spencer, D. C., "A theorem of completeness for complex analytic fibre spaces," Acta Math., 100 (1958), 281–294.
Kuranishi, M., "On the locally complete families of complex analytic structures," Ann. Math. (2), 75 (1962), 536–577, MR 25 #4550.
Kuranishi, M., "New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis 1964), Springer-Verlag, Berlin-Heidelberg New York, 1965, 142–154, MR 31 #768.
Kuranishi, M., "Deformations of compact complex manifolds," Presses de l'Université de Montreal (1969)
Lichtenbaum, S., Schlessinger, M., "The cotangent complex of a morphism," Trans. Amer. Math. Soc., 128 (1967), 41–70, MR 25 #4550.
Mandelbaum, R., "Four dimensional topology: an introduction," Bull. A.M.S. (1980), 1–159.
Mather, J. N., "Stable map germs and algebraic geometry," Manifolds-Amsterdam, 1970, Springer L.N.M. 197 (1971), 176–193.
Mather, J. N., "Generic projections," Annals of Math., 98 (1973), 226–245.
Matsumura, H., "On algebraic groups of birational transformations," Rend. Accad. Lincei Ser. 8, 34 (1963), 151–155.
Milnor, J., Stasheff, J., "Characteristic classes," Ann. Math. Studies 76, Princeton Univ. Press, Princeton (1974).
Moishezon, B. G., "On n-dimensional compact varieties with n algebraically independent meromorphic functions," Izv. Ak Nauk SSSR Ser. Mat. 30 (1966), 133–144, 345–386, 621–656. English transl., Am. Math. Soc. Transl. (2), 63 (1967), 51–177.
Moishezon, B. G., "An algebraic analogue to compact complex spaces with a sufficiently large field of meromorphic functions. Izv. Akad. Nauk SSSR Ser. Mat., 33 (1969), 174–238, 323–367, 506–548.
Mumford, D., "Further pathologies in algebraic geometry," Am. J. Math. 84 (1962), 642–648.
Mumford, D., "Geometric invariant theory," 2nd edition (1982), with J. Fogarthy coauthor), Heidelberg, Springer (1965).
Mumford, D., "Lectures on curves on an algebraic surface," Annals of Math. Studies 59, Princeton Univ. Press, Princeton (1966).
Nakamura, L., "VII0 surfaces and a duality of cusp sirgularities," in Classification of algebraic and analytic manifolds. Proc. Katata Symp. 1982, P.M. 39, Birkhäuser (1983), 333–378.
Nakamura, I., "On surfaces of class VIIo with curves," Inv. Math. 78, 3 (1984), 393–443.
Noether, M., "Zur theorie des eindeutigen Entsprechens algebraischer Gebilde," Math. Ann., 2 (1870), 293–316, 8 (1875), 495–533.
Noether, M., "Anzahl der Moduln einer Classe algebraischer Flächen," Sb. Kgl. Preuss. Akad. Wiss. Math.-Nat. Kl., Berlin (1888), 123–127.
Palamodov, V. P., "Deformations of complex spaces," Uspekhi Mat. Nauk. 31:3 (1976), 129–194. Transl. Russian Math. Surveys 31:3 (1976), 129–197.
Persson, U., "An introduction to the geography of surfaces of general type," Proc. of A.M.S. Conf. in Algebraic Geometry, 1985.
Popp, H., "Moduli theory and classification theory of algebraic varieties," Springer L.N.M. 620 (1977).
Pourcin, G., "Déformation de singularités isolées, Astérisque, Soc. Math. France 16 (1974), 161–173.
Ramanujam, C. P., "Remarks on the Kodaira vanishing theorem," J. Indian Math. Soc., 36 (1972), 41–51; supplement in J. Indian Math. Soc. 38 (1974), 121–124.
Reider, I., "Bounds on the number of moduli for irregular surfaces of general type," Manuscr. Math.
Reider, L., "Linear systems and vector bundles of rank 2 on surfaces" Annals of Math., to appear.
Rokhlin, V. A., "New results in the theory of 4-dimensional manifolds," Dokl. Akad. Nauk. SSSR, 84 (1952), 221–224.
Rossi, H., "Vector fields on analytic spaces," Annals of Math. 78, 3 (1963), 455–467.
Schlessinger, M., "Functors of Artin rings," Trans. Amer. Math. Soc., 130 (1968), 208–222, MR 36 #184.
Seiler, W.K., "Global Moduli for Elliptic Sufaces with a Section," Comp. Math. 62 (1987), 169–185.
Seiler, W.K., "Global Moduli for Polarized Surfaces," Comp. Math. 62 (1987) 187–213.
Seiler, W.K., "Deformation of Weierstraß Elliptic Surfaces," Math. Annal. 1988
Sernesi, E., "Small deformations of global complete intersections," B.U.M.I., 12 (1975), 138–146.
Sernesi, E., "Sullo schema di Hilbert," preprint.
Serre, J.-P., "Faisceaux algébriques coherents," Ann. Math., 61 (1955), 197–278.
Serre, J.-P., "Cours d'arithmetique," Presses Universitaires de France, Paris (1970).
Shafarevitch, L., et al., "Algebraic surfaces," Proc. Steklov Inst., A.M.S. Translation (1967), Providence.
Siegel, C. L., "Meromorphe Funktionen auf kompakten analytischen Mannigfaltigkeiten, Nachr. Akad. Wiss. Göttingen, math-phys. Klasse 4 (1955), 71–77.
Siu, T. Y., "Every K-3 surface is Käbler," Inv. Math., 73 (1983), 139–150.
Spivak, M., "(A comprehensive introduction to) Differential Geometry," II ed., vol. I–V, Publish or Perish, Berkeley (1979).
Suwa, T., "Stratification of local moduli spaces of Hirzebruch manifolds," Rice University Studies 59 (1975), 129–146, MR 48 #4362.
Tjurina, G. N., "Resolution of singularities of flat deformations of rational doublets," Funktsional. Anal. i Prilozhen., 4 (1) (1970), 77–83, MR 42 #2031.
Todorov, A., "Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3-surfaces," Invent. Math., 81 (1980), 251–266.
Usui, S., "Deformations and local Torelli theorem for certain surfaces of general type," in Algebraic Geometry, Copenhangen 1978, Springer L.N.M. 732 (1979), 605–623.
Wahl, S., "Deformations of plane curves with nodes and cusps," Am. J. Math., 96 (1974), 529–577.
Wavrik, J. J., "Obstructions to the existence of a space of moduli," Global Analysis, Princeton Math. Series 29 (1969), 403–414.
Weil, A., "Introduction a l'etude des varietes Kähleriennes," Hermann, Paris (1958).
Yau, S. T., "Calabi's conjecture and some new results in algebraic geometry," Proc. Nat. Acad. Sci. U.S.A., 74 (1977), 1798–1799.
Zariski, O., "Algebraic surfaces, 2nd ed. Erg. Math. 61, Springer, Heidelberg (1971).
Zappa, G., "Sui Sistemi continui di curve sopra una rigata algebrica," Gior. Mat. Battaglini, 77 (1947).
Zappa, G., "Sulla degenerazione delle superficie algebriche in sistemi di piani distinti, con applicazioni allo studio de llerigate," Atti Accad. Naz. Lincei Mem., 13 (1942).
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Catanese, F. (1988). Moduli of algebraic surfaces. In: Sernesi, E. (eds) Theory of Moduli. Lecture Notes in Mathematics, vol 1337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082806
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