Bi-algebraic geometry of strata of differentials in genus zero
arXiv:2310.07523 · doi:10.1112/S0010437X2400770X
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.
32 pages