Type II Degenerations of K3 Surfaces of Degree 4
Algebraic Geometry
2025-02-27 v2
Abstract
We study Type II degenerations of K3 surfaces of degree 4 where the central fiber consists of two rational components glued along an elliptic curve. Such degenerations are called Tyurin degenerations. We construct explicit Tyurin degenerations corresponding to each of the 1-dimensional boundary components of the Baily-Borel compactification of the moduli space of K3 surfaces of degree 4. For every such boundary component we also construct an 18-dimensional family of Tyurin degenerations of K3 surfaces of degree 4 and compute the stable models of these degenerations.
Keywords
Cite
@article{arxiv.2502.04301,
title = {Type II Degenerations of K3 Surfaces of Degree 4},
author = {James Matthew Jones},
journal= {arXiv preprint arXiv:2502.04301},
year = {2025}
}
Comments
28 pages, 1 figure. v2: Corrected the equation defining the family in section 3.4, plus some other minor changes; mathematical results unaffected