Counting Lines with Vinberg's algorithm
Algebraic Geometry
2025-05-19 v2
Abstract
We combine classical Vinberg's algorithms with the lattice-theoretic/arithmetic approach from arXiv:1706.05734 [math.AG] to give a method of classifying large line configurations on complex quasi-polarized K3-surfaces. We apply our method to classify all complex K3-octic surfaces with at worst Du Val singularities and at least 32 lines. The upper bound on the number of lines is 36, as in the smooth case, with at most 32 lines if the singular locus is non-empty.
Cite
@article{arxiv.2104.04583,
title = {Counting Lines with Vinberg's algorithm},
author = {Alex Degtyarev and Sławomir Rams},
journal= {arXiv preprint arXiv:2104.04583},
year = {2025}
}
Comments
Minor misprints corrected (a.o. in formulation of Lemma 2.29). Extra explanation added to various parts of the text. Scripts for all computer-aided computations added as ancillary files. The changes result in no alterations of main results of the paper