Nodal quintic surfaces and lines on cubic fourfolds (with an appendix by John Christian Ottem)

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 (1979), Murre (1972), and Voisin (1986), Results due to Shen (2012, 2014) 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.