Line arrangements, operators and elliptic modular surfaces

by Prof. Xavier Roulleau (University of Angers)

Thursday 27 Mar 2025, 08:30 → 10:30 Europe/Paris

Thursday 27 March 2025, 4:30 PM - 6:30 PM (Korea)

Arrangements of lines in the projective plane—finite unions of lines—arise in various branches of mathematics, including topology, algebra, and combinatorics. Many questions remain open. For instance, the complete classification of complex arrangements without double points is still unknown, as is the full list of real simplicial arrangements, where the regions formed by the lines are exclusively triangles.

To generate new line arrangements with interesting properties, we introduce operators acting on the set of plane line arrangements.

In this talk, I will present examples of moduli spaces of line arrangements that are preserved by certain such operators. In particular, we will see that the elliptic surface K₁(n) over the modular elliptic curve X₁(n) —which parametrizes elliptic curves with a torsion point of order n > 3— can also be interpreted as (the compactification of) the moduli space of certain line arrangements.

We will explore the existence of an operator acting on these arrangements and, consequently, on the elliptic surface K₁(n), and describe its action on the surface.

Work in collaboration with Lukas Kühne (Bielefeld).

LINK FOR THE WEBINAR

https://cnrs.zoom.us/j/99809114553?pwd=QBsnIaRBLtIvpHR8dJHlH7VE6d1XTm.1