Geometry Seminar
University of Tor Vergata, Department of Mathematics
4th of March 2025, 14:30-16:00,room D’Antoni
Algorithms for plane algebraic curves, with an application to integrating algebraic functions
Nicolas Mascot
Trinity College Dublin
We will outline an efficient algorithmic approach to the desingularisation of plane algebraic curves. Applications include computing the genus, Riemann-Roch spaces, and testing whether the curve is hyperelliptic. Afterwards, we will see that the (apparently rustic-looking) problem of finding the antiderivative of an algebraic function is actually related to the (much cooler-sounding) ability to test whether certain divisors are torsion in the Picard group of a curve. We will show how to achieve this thanks to the algorithms outlined earlier, which will lead us to a complete integration algorithm for algebraic functions based on arithmetic geometry. The talk will feature may explicit examples. |