Effective Double Covers

01/07/2023 to 31/12/2024

Double covers play a central role in the study of algebraic curves since more than a century,
first from an analytic and then from an algebraic point of view. On one hand, they represent a
fundamental part of the theory, as they are the first interesting maps of curves that one can
study beyond isomorphisms. On the other hand, they can be described very concretely and
explicitly. In this project, we propose to study double covers from curves from an effective point of view, aiming from
theoretical as well as computational results. More precisely, we will aim at two directions, that
we describe afterwards in more detail:

• Effective Prym-Torelli for étale double covers.
• Canonical double covers.