This subtopic studies holomorphic functions, covering core complex analytic properties, local behavior, and global function-theoretic phenomena.

This subtopic studies local analytic geometry, focusing on germs, local rings, and the structure of complex-analytic singularities.

This subtopic studies analytic spaces, including local and global analytic structures that generalize complex manifolds and varieties.

This subtopic studies real methods and analytic continuation, emphasizing continuation principles and real-variable techniques in complex analysis.

This subtopic studies holomorphic convexity, describing convexity properties in complex analysis and their consequences for function theory.

This subtopic studies deformations and moduli in complex analysis and geometry, focusing on families of analytic structures and parameter spaces.

This subtopic studies holomorphic mappings, including mapping problems, extension phenomena, and qualitative properties of complex-analytic maps.

This subtopic studies compact analytic spaces, where compactness influences global complex-analytic structure and function theory.

This subtopic studies fiber spaces and vector bundles in complex analysis and geometry, linking local linear data with global analytic structure.

This subtopic studies complex manifolds, emphasizing complex structures, holomorphic coordinates, and the geometry of smooth complex spaces.

This subtopic studies singularities, focusing on local structure, resolution, and analytic classification of non-regular points.

This subtopic studies differential operators in complex analysis, connecting analytic PDE methods with holomorphic function theory and complex geometry.