Nodal quintic surfaces and lines on cubic fourfolds
Abstract
We study nodal quintic surfaces with an even set of 16 nodes as analogues of singular Kummer surfaces. The interpretation of the natural double cover of an even 16-nodal quintic as a certain Fano variety of lines could be viewed as a replacement for the additive structure of the cover of a singular Kummer surface by its associated abelian surface. Most of the results in this article can be seen as refinements of known facts and our arguments rely heavily on techniques developed by Beauville, Murre, and Voisin. Results due to Izadi and Shen are particularly close to some of the statements. In this sense, the text is mostly expository (but with complete proofs), although our arguments often differ substantially from the original sources.
Cite
@article{arxiv.2108.10532,
title = {Nodal quintic surfaces and lines on cubic fourfolds},
author = {Daniel Huybrechts and with an appendix by John Ottem},
journal= {arXiv preprint arXiv:2108.10532},
year = {2023}
}
Comments
27 pages. This revision includes an appendix by J. Ottem in which the double cover is proved to be topologically (and not only algebraically) simply connected. Minor mistakes fixed