The 22 periods of a quartic surface

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).