The Only Complex 4-Net Is the Hesse Configuration
Algebraic Geometry
2020-04-21 v2 Combinatorics
Abstract
It has been conjectured that the only nets realizable in are 3-nets and the Hesse configuration (up to isomorphism). We prove this conjecture.
Cite
@article{arxiv.2002.02660,
title = {The Only Complex 4-Net Is the Hesse Configuration},
author = {Alp Bassa and Ali Ulas Ozgur Kisisel},
journal= {arXiv preprint arXiv:2002.02660},
year = {2020}
}
Comments
We change the (previously wrong) construction of the multi-cyclic cover. In the new construction singularities appear and resolving them gives a contribution to the signature. This changes some of the calculations, however all results in the previous version concerning existence of nets remain true