References
Aeppli, A.: Modifikation von reellen und komplexen Mannigfaltigkeiten. Comment. Math. Helv.31, 219–301 (1957)
Arnold, V.: Normal forms for functions near degenerate critical points, the Weyl groups ofA k ,D k ,E k , and Lagrangian singularities. Functional Anal. Appl.6, 254–272 (1972)
Artin, M.: Some numerical criteria for contractability of curves on algebraic surfaces. Amer. J. Math.84, 485–496 (1962)
Artin, M.: On isolated rational singularities of surfaces. Amer. J. Math.88, 129–136 (1966)
Bombieri, E., Husemoller, D.: Classifications and embeddings of surfaces. Proc. Symp. Pure Math. 29. Algebraic Geometry, Azcata (1974)
Brenton, L.: Some algebraicity criteria for singular surfaces. Invent. Math.41, 129–147 (1977)
Brenton, L.: On the Riemann-Roch equation for singular surfaces. Pacific J. Math.71, 299–312 (1977)
Brenton, L.: Some examples of singular compact analytic spaces which are homotopy equivalent to the complex projective plane. Topology16, 423–433 (1977)
Brenton, L.: On singular complex surfaces with vanishing geometric genus, and pararational singularities. To appear
Brenton, L., Morrow, J.: CompactifyingC n. Proc. Symp. Pure Math.30, Several Complex Variables, Williams College I, 241–246 (1977)
Brenton, L., Morrow, J.: Compactifications ofC n. Trans. Amer. Math. Soc.246, 139–153 (1978)
Burns, D.: On rational singularities in dimensions >2. Math. Ann.211, 237–244 (1974)
Du Val, P.: On isolated singularities of surfaces which do not affect the condition of adjunction. Proc. Cambridge Philos. Soc.30, 453–491 (1933/1934)
Kodaira, K.: On Kähler varieties of restricted type. Ann. of Math.60, 28–48 (1954)
Kodaira, K.: On the structure of compact complex analytic surfaces, I–IV. Amer. J. Math.86, 751–798 (1964);88, 682–721 (1966);90, 55–83 and 1048–1065 (1968)
Kodaira, K.: Holomorphic mappings of polydiscs into compact complex manifolds. J. Differential Geometry6, 33–46 (1971)
Kume, S., Watanabe, K.: On certain rational double points in dimensions >2. Sci. Rep. T.K.D. Sect. A.13, 21–28 (1977)
Laufer, H.: On rational singularities. Amer. J. Math.94, 597–608 (1972)
Laufer, H.: Taut two-dimensional singularities. Math. Ann.205, 131–164 (1973)
Laufer, H.: On μ for surface singularities. Proc. Symp. Pure Math.30, Several Complex Variables, Williams College 45–49 (1977)
Laufer, H.: On minimally elliptic singularities. Amer. J. Math.99, 1257–1295 (1977)
Laufer, H.: On ¶1 as an exceptional set, to appear in the Proceedings of the Conference on Complex Analysis, Princeton, 1979 (Annals of Math. Studies series)
Moisheson, B.: Onn-dimensional compact complex varities withn algebraically independent meromorphic functions. Amer. Math. Soc. Transl.63, 51–177 (1967)
Morrow, J.: Minimal normal compactifications ofC 2. Proc. Conf. on Complex Analysis, Rice Univ. Stud.59, 97–112 (1973)
Morrow, J., Rossi, H.: Some theorems of algebraicity for complex spaces. J. Math. Soc. Japan27, 167–183 (1975)
Ramanujam, C.P.: A characterization of the affine plane as an algebraic variety. Ann. of Math.94, 69–88 (1971)
Remmert, R., Van de Ven, T.: Zwei Sätze über die komplexprojektive Ebene. Nieuw. Arch. Wisk.8, 147–157 (1960)
Van de Ven, A.: Analytic compactifications of complex homology cells. Math. Ann.147, 189–204 (1962)
Author information
Authors and Affiliations
Additional information
This research was supported in part by National Science Foundation Research Grant No. MCS 77-03540
Rights and permissions
About this article
Cite this article
Brenton, L. On singular complex surfaces with negative canonical bundle, with applications to singular compactifications ofC 2 and to 3-dimensional rational singularities. Math. Ann. 248, 117–124 (1980). https://doi.org/10.1007/BF01421952
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01421952