The 22 periods of a quartic surface

E1 05 (Leibniz-Saal)


A smooth complex quartic surface in the projective 3-space defines 22 complex numbers called periods. The integer relations between them describe the algebraic curves lying on this surface, in the form of the Néron-Severi group. I will explain how to compute numerically the periods with thousands of digits of precision and recover heuristically the lattice of integer relations. This provides an insight on the Néron-Severi group that purely algebraic methods fail to provide.

This is joint work with Eric Pichon-Pharabod (Inria), Emre Sertöz (Leiden University) and Pierre Vanhove (CEA).


Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Johannes Henn

Max Planck Institute for Physics

Bernd Sturmfels

Max-Planck-Institut für Mathematik in den Naturwissenschaften