Post History
#3: Question closed
by
ArtOfCode
·
2026-04-24T08:52:49Z (5 months ago)
#2: Post edited
by
zetaspace
·
2026-04-18T23:03:17Z (5 months ago)
Algebraic Geometry Resources that study this triple?
- Algebraic geometry references that study this triple?
A seed- $$ \mathcal S = (\mathcal I, \Gamma, \Pi) $$
- 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?
- 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?
#1: Initial revision
by
zetaspace
·
2026-04-17T19:19:13Z (5 months ago)
Algebraic Geometry Resources that study this triple?
A seed
$$ \mathcal S = (\mathcal I, \Gamma, \Pi) $$
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?