1. Bi-algebraic geometry of strata of differentials in genus zero
- Author
-
Benirschke, Frederik
- Subjects
Mathematics - Algebraic Geometry - Abstract
We study algebraic subvarieties of strata of differentials in genus zero satisfying algebraic relations among periods. The main results are Ax-Schanuel and Andr\'e-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 Teichm\"uller curves., Comment: 32 pages
- Published
- 2023