Resolution of singularities of double covers of regular surfaces

Abstract: In this talk I will explain how to apply Lipman's method to resolve the singularities of double covers of regular surfaces. This leads in particular to an algorithm to finding a regular model over the ring of integers for hyperelliptic curves defined over the rational numbers. Such a regular model contains quite a few interesting information concerning the arithmetical properties of the curves.

algebraic geometrynumber theory

Audience: researchers in the topic

Luxembourg Number Theory Day 2024