Rational points in the Noether-Lefschetz locus of moduli spaces of K3 surfaces
Algebraic Geometry
2023-03-29 v2 Number Theory
Abstract
In this paper, we study maps between moduli spaces of lattice-polarized K3 surfaces induced by sublattices of prime index. We show that these maps can be used to determine if a rational point of the moduli space belongs to the Noether-Lefschetz locus. As an application, we prove that the Bombieri-Lang conjecture implies non-density statements for the rational points in the Noether-Lefschetz locus, as predicted by a conjecture of Shafarevich.
Keywords
Cite
@article{arxiv.2210.07375,
title = {Rational points in the Noether-Lefschetz locus of moduli spaces of K3 surfaces},
author = {Domenico Valloni},
journal= {arXiv preprint arXiv:2210.07375},
year = {2023}
}
Comments
Improved exposition and results