Complete subvarieties in the projectivized strata of meromorphic differentials

2025/11/10 by Chen, Dawei, Tahar, Guillaume
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.2511.07102

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

Here we give an explicit construction of a globally defined strictly plurisubharmonic function on projectivized strata of strictly meromorphic differentials with prescribed orders of zeros and poles. In particular, this yields a flat-geometric proof that these strata do not contain positive-dimensional complete subvarieties.

Citations

• Nonvarying, affine, and extremal geometry of strata of differentials
• Complete curves in the strata of differentials
• Strata of k-differentials
• Counting saddle connections in flat surfaces with poles of higher order
• Teichmüller dynamics in the eyes of an algebraic geometer
• Translation surfaces and their orbit closures: An introduction for a\n broad audience
• Connected components of the strata of the moduli space of meromorphic differentials

Related

• Complete curves in the strata of differentials
• Uniruledness of Strata of Holomorphic Differentials in Small Genus
• Nonvarying, affine, and extremal geometry of strata of differentials
• Completeness in Partial Differential Fields
• Flat Projective Structures on Surfaces and Cubic Holomorphic Differentials