Linfoot seminar: Computing the Abel-Jacobi map on complex hyperelliptic curves
Pascal Molin (Université Paris 7)
4th Floor Seminar Room (Howard House)
We propose an efficient algorithm to compute the period lattice and the Abel-Jacobi map of hyperelliptic curves. The method relies on rigorous numerical integration on carefully chosen paths, and allows to reach thousands of digits of accuracy for diophantine or cryptographic applications. The same strategy applies to superelliptic curves of the form y^m=f(x), and scales very well in terms of the genus (this is joint work with C. Neurohr).