Separation of periods of quartic surfaces

Pierre Lairez (1) , Emre Can Sertöz (2)

1 SPECFUN - Symbolic Special Functions : Fast and Certified
2 MPIM - Max Planck Institute for Mathematics

The periods of a quartic surface X are complex numbers obtained by integrating a holomorphic 2-form over 2-cycles in X. For any quartic X defined over the algebraic numbers and any 2-cycle G in X, we give a computable positive number c(G) such that the associated period A satisfies either |A| > c(G) or A = 0. This makes it possible in principle to certify a part of the numerical computation of the Picard group of quartics and to study the Diophantine properties of periods of quartics.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Pierre Lairez, Emre Can Sertöz. Separation of periods of quartic surfaces. 2020. ⟨hal-03022612v1⟩