We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.
In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.
In questo lavoro si generalizzano alcuni risultati di [3] riguardanti la proprietà di alcune curve nodali, su superficie non-singolari in , di essere «geometricamente linearmente normali» (concetto che estende la ben nota proprietà di essere linearmente normale). Precisamente, per una data curva , irriducibile e dotata di soli punti nodali come uniche singolarità, che giace su una superfice proiettiva, non-singolare e linearmente normale, si determina un limite superiore «sharp» sul numero dei...
Let be a smooth projective curve over an algebraically closed field of characteristic . Consider the dual pair over with split. Write and for the stacks of -torsors and -torsors on . The theta-kernel on yields theta-lifting functors and between the corresponding derived categories. We describe the relation of these functors with Hecke operators. In two particular cases these functors realize the geometric Langlands functoriality for the above pair (in the non ramified case)....