Holomorphic symmetric differentials and parallelizable compact complex manifolds

2019/05/26 by Ernesto C. Mistretta, Mistretta, Ernesto C.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1905.10849

openalex publication_date 2019/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a characterization of complex tori using holomorphic symmetric differentials. With the same method we show that compact complex manifolds of Kodaira dimension 0 having some symmetric power of the cotangent bundle globally generated are quotients of parallelizable manifolds, therefore have an infinite fundamental group.

Citations

• Complex parallisable manifolds

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