Diagonal Quotient Surfaces
نویسنده
چکیده
Let X be a smooth projective curve over C which admits a finite group G of automorphisms. Then G×G acts on the product surface Y = X ×X, and so for each subgroup H ≤ G×G, the quotient Z = H\Y is a normal algebraic surface. Here we shall restrict attention to the case that the subgroup H is the graph of a group automorphism α ∈ Aut(G) of G, i.e. H = ∆α = {(g, α(g)) : g ∈ G}; we propose to call the resulting quotient surface a (twisted) diagonal quotient surface, and denote it by ZX,G,α = ∆α\Y.
منابع مشابه
Modular Diagonal Quotient Surfaces
Notes: 1) The modular diagonal quotient surfaces as defined above may be viewed as a special case of the general diagonal quotient surfaces studied in Kani/Schanz[7]. 2) The inclusions of subsgroups {1} ≤ ∆αε ≤ G × G induce finite morphisms (both of degree m = |G|) YN Φ → ZN,ε Ψ → Y1 ' P × P. Moreover, by using Shimura’s canonical model X(N)/Q, it can be shown that all these varieties have cano...
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