On the Structure of Compact Complex Analytic Surfaces, II

1966/07/01 by K. Kodaira · 10 citations
Mathematics · Engineering · #Mathematics and Applications #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic and Geometric Analysis #Mathematics #Pure mathematics #Geometry

paper · doi:10.2307/2373150

openalex publication_date 1966/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

This note is a continuation of our previous report' on the structure of compact complex analytic surfaces.5. We shall employ the notation of our previous report.Thus we denote by S a surface and by b,, CP, pa, q, ..., respectively, the vth Betti number, the Ath Chern class, the geometric genus, the irregularity,... of S. Any complex line bundle over a regular surface is determined uniquely by its Chern class.Hence, a regular surface is a K3 surface if and only if its first Chern class vanishes.It follows that any deformation of a K3 surface is a K3 surface.In this section we shall outline a proof of the following theorem which has been conjectured earlier by A. Weil and independently by A. Andreotti.'THEOREM 9. Every K3 surface is a deformation of a nonsingular quartic surface in a projective 3-space.

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• Langlands Reciprocity for Algebraic Surfaces
• Constructions and classifications of projective Poisson varieties
• Enriques–Kodaira classification [wikipedia]
• Hopf surface [wikipedia]