On singular complex surfaces with negative canonical bundle, with applications to singular compactifications of \(\mathbb C^2\) and to 3-dimensional rational singularities

DOI10.1007/BF01421952zbMath0407.14013MaRDI QIDQ1257937

Lawrence Brenton

Publication date: 1980

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163372

zbMATH Keywords

Gorenstein singularitiescanonical line bundleclassification of compact complex analytic surfacesrational Gorenstein singularity

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Families, moduli, classification: algebraic theory (14J10) Compact complex surfaces (32J15)

Related Items

Ample divisors on normal Gorenstein surfaces, Singular Del Pezzo surfaces and analytic compactifications of 3-dimensional complex affine space C³, Normal Analytic Compactifications of $$\mathbb{C}^{2}$$, K-stable smooth Fano threefolds of Picard rank two, On higher dimensional complex Plateau problem, Unnamed Item, Unnamed Item, Log del Pezzo surfaces with not small fractional indices, Notes on minimal compactifications of the affine plane, \(K\)-stability of cubic threefolds, Rational mappings of Del Pezzo surfaces, and singular compactifications of two-dimensional affine varieties

Cites Work

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• Modifikation von reellen und komplexen Mannigfaltigkeiten
• Analytic compactifications of complex homology cells
• Some theorems of algebraicity for complex spaces
• On the Riemann-Roch equation for singular complex surfaces
• Some examples of singular compact analytic surfaces which are homotopy equivalent to the complex projective plane
• Ambient deformations for exceptional sets in two-manifolds
• Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
• Taut two-dimensional singularities
• A topological characterisation of the affine plane as an algebraic variety
• Holomorphic mappings of polydiscs into compact complex manifolds
• On Kähler varieties of restricted type. (An intrinsic characterization of algebraic varieties.)
• Compactifications of C n
• Some Numerical Criteria for Contractability of Curves on Algebraic Surfaces
• On Minimally Elliptic Singularities
• On the Structure of Compact Complex Analytic Surfaces, I
• On Isolated Rational Singularities of Surfaces
• On Rational Singuarities