A descent method for explicit computations on curves

Document Type : Research Paper


Department of Mathematical Sciences‎, ‎Sharif University of Technology‎, ‎Tehran‎, ‎Iran.


‎It is shown that the knowledge of a surjective morphism $X\to Y$ of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of $j(n\tau)$ (for some small $n$) in terms of $j(\tau)$ for the elliptic curve ‎with period lattice $(1,\tau)$‎, ‎the period matrix for the Jacobian of a family of genus-$2$ curves‎ ‎complementing the classic calculations of Bolza‎ ‎and explicit general formulae for branched covers of an elliptic curve with exactly one ramification point.


Main Subjects

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