Characters and Automorphism Groups of Compact Riemann Surfaces

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Standard isotrivial fibrations with p_g=q=1, II (2007, methodology): “in Proposition 1.3. For any h ∈ G set H := hhi and deﬁne FixX(h) = FixX(H) := {x ∈ X | hx = x}. Proposition 1.4. If o(h) = m then FixX(h) = |NG(H)| · X 1≤i≤r m|m i H∼ G hg mi/m i i 1 mi . Proof. (See [Bre00], Lemma 10.4). Let x be in FixX(h) and let Ri be a set of coset representatives of hgii in G.”
Group actions on Jacobian varieties (2003, background): “tten (t+1) relations after the colon. Furthermore, the covering τ : ∆ → ∆/Γ = S/G has branch values in a ﬁnite set {qj,j = 1,...,t} and its ramiﬁcation index is mj for each j. Moreover, according to ([1], §3.2, p. 8), the stabilizers of the points in the ﬁber τ−1(q j) are the subgroups in the conjug”
The locus of curves with prescribed automorphism group (Communications in Arithmetic Fundamental Groups) (2002, methodology): “Using computational group theory (more precisely, the computer algebra system GAP [9]), Breuer [5] extended this up to genus 48: Computing all groups G ≤ Aut( X g ) together with their character on the space of holomorphic diﬀerential forms.”
Shimura varieties in the Torelli locus via Galois coverings of elliptic curves (2014, unknown): “Recall that the action of the mapping class group Map1,[2] on Γ1,2 is generated (up to inner automorphism) by the seven moves described in [34, Proposition 1.14] – from where we also borrow the notation.”