10 papers
Construction of free arrangements using point-line operators
Piotr Pokora, Xavier Roulleau
We construct new examples of free curve arrangements in the complex projective plane using point-line operators recently defined by the second author. In particular, we construct a…
Dynamical systems on some elliptic modular surfaces via operators on line arrangements
Lukas Kühne, Xavier Roulleau
This paper further studies the matroid realization space of a specific deformation of the regular -gon with its lines of symmetry. Recently, we obtained that these particular re…
Regular polygons, line operators, and elliptic modular surfaces as realization spaces of matroids
Lukas Kühne, Xavier Roulleau
For an integer , we investigate the matroid realization space of a specific deformation of the regular -gon along with its lines of symmetry. It turns out that this par…
On a sequence of singular ball quotient surfaces on the line
Carlos Rito, Xavier Roulleau
Starting from computer experiments with the fundamental group of the Cartwright--Steger surface, we construct an infinite tower of normal projective surfaces obtai…
Pluri-cotangent maps of surfaces of general type
Francesco Polizzi, Xavier Roulleau
Let be a compact, complex surface of general type whose cotangent bundle is strongly semi-ample. We study the pluri-cotangent maps of , namely the morphisms $Ï_n \co…
Number of partitions of modular integers (with an Appendix by P. Deligne)
David Broadhurst, Xavier Roulleau
For integers , we give a formula for the number of order subsets of the ring whose sum of elements is modulo . To do so, we de…