Algebraic geometry references that study this triple? [closed]
Closed as unclear by ArtOfCode on Apr 24, 2026 at 08:52
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A seed (for lack of a better name)
$$ \mathcal S = (\mathcal I, \Gamma, \Pi) $$is a $\Pi$-equivariant 4-sheeted branched cover
$$ p: \mathcal I \to \widehat{\Bbb C} $$
equipped with a distinguished embedded graph
$$ \Gamma \subset \mathcal I $$representing the intrinsic degeneration locus.
Question. Hurwitz theory, the theory of D'essins, and related areas all seem to focus on particular objects within the triple of $\mathcal S$, but I am unaware of a program that collects them into one object and studies them holistically.
Are there resources that I've possibly missed, that do specifically study the triple $$\mathcal S = (\mathcal I, \Gamma, \Pi)$$
especially when the generators $\pi \in \Pi$ are defined as piecewise mappings?
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