Bi-algebraic geometry of strata of differentials in genus zero

2023/10/11 by Frederik Benirschke, Benirschke, Frederik
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2310.07523

openalex publication_date 2023/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study algebraic subvarieties of strata of differentials in genus zero satisfying algebraic relations among periods. The main results are Ax-Schanuel and André-Oort-type theorems in genus zero. As a consequence, one obtains several equivalent characterizations of bi-algebraic varieties. It follows that bi-algebraic varieties in genus zero are foliated by affine-linear varieties. Furthermore, bi-algebraic varieties with constant residues in strata with only simple poles are affine-linear. Additionally, we produce infinitely many new linear varieties in strata of genus zero, including infinitely many new examples of meromorphic Teichmüller curves.

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