English

One-dimensional Local Families of Complex K3 Surfaces

Algebraic Geometry 2024-06-04 v1

Abstract

For any complex K3 surface XX, we construct a one-dimensional deformation in which all integers ρ\rho with 0ρ200 \leq \rho \leq 20 occur as Picard numbers of some fibres. In contrast, we prove that the generic one-dimensional local family of K3 surfaces admits only 00 and 11 as Picard numbers of the fibres.

Keywords

Cite

@article{arxiv.2209.13003,
  title  = {One-dimensional Local Families of Complex K3 Surfaces},
  author = {Riccardo Carini and Francesco Viganò},
  journal= {arXiv preprint arXiv:2209.13003},
  year   = {2024}
}

Comments

10 pages, 4 figures