Separation of periods of quartic surfaces
Algebraic Geometry
2023-09-20 v3 Number Theory
Abstract
We give a computable lower bound on the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determination of height bounds on components of the Noether--Lefschetz loci. This makes it possible to study the Diophantine properties of periods of quartic surfaces and to certify a part of the numerical computation of their Picard groups.
Keywords
Cite
@article{arxiv.2011.12316,
title = {Separation of periods of quartic surfaces},
author = {Pierre Lairez and Emre Can Sertöz},
journal= {arXiv preprint arXiv:2011.12316},
year = {2023}
}
Comments
28 pages. Added a final section elaborating on our results. Implemented referee suggestions. Final version