Classification of Projective Models of K3-surfaces
Abstract
Extending the methods previously established for plane sextics and quartic surfaces, we develop a unified and systematic framework for the equisingular deformation classification of projective models of K3-surfaces of arbitrary polarization. We treat all polarizations of degree 2n with n≤ 4, including the higher-degree cases of sextic surfaces in ℙ4 and octic surfaces in ℙ5. The computational machinery developed here is degree-independent and provides a complete tool for enumerating and distinguishing the deformation classes arising from singular projective models of K3-surfaces. This framework lays the foundation for future investigations in higher degrees, particularly the geometry of equisingular strata, extremal configurations, real structures.
Related
- Smooth projective surfaces with bounded cohomology property II
- Dynamics on projective K3 surfaces: Herman rings
- Deformations of the logarithmic tangent bundle of smooth projective surfaces
- Branched real projective structures on surfaces and geometrisation of representations
- Effective Results for Foliations on Smooth Projective Complete Intersection Surfaces
BibTeX
@misc{aktas2026classification,
title = {{Classification of Projective Models of $K3$-surfaces}},
author = {Çisem Güneş Aktaş},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16408},
eprint = {2610.16408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16408},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classification of Projective Models of K3-surfaces
AU - Çisem Güneş Aktaş
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16408
UR - https://arxiv.org/abs/2610.16408
AB - Extending the methods previously established for plane sextics and quartic surfaces, we develop a unified and systematic framework for the equisingular deformation classification of projective models of K3-surfaces of arbitrary polarization. We treat all polarizations of degree 2n with n≤ 4, including the higher-degree cases of sextic surfaces in ℙ^4 and octic surfaces in ℙ^5. The computational machinery developed here is degree-independent and provides a complete tool for enumerating and distinguishing the deformation classes arising from singular projective models of K3-surfaces. This framework lays the foundation for future investigations in higher degrees, particularly the geometry of equisingular strata, extremal configurations, real structures.
ER -