Veech fibrations

Sam Freedman; Trent Lucas

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arXiv · 2310.02325

Veech fibrations

Sam Freedman·Trent Lucas

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Abstract

We investigate complex surfaces that fiber over Teichm\"uller curves where the generic fiber is a Veech surface. When the fiber has genus one, these surfaces are elliptic fibrations; for higher genus fibers, they are typically minimal surfaces of general type. We compute the topological and complex-geometric invariants of these surfaces via the monodromy action on the mod-$m$ homology of the fiber. We get exact values of the invariants for all known algebraically primitive Teichm\"uller curves.

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Sam Freedman, Trent Lucas. 2023-10-03. Veech fibrations. https://arxiv.org/abs/2310.02325

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