Edge and Fano on nets of quadrics

Abstract

In a number of papers by Edge, and in a related paper by Fano, several properties are discussed about the family of scrolls R ⊂ P 3 of degree 8 whose plane sections are projected bicanonical models of a genus 3 curve C. This beautiful classical subject is implicitely related to the moduli of semistable rank two vector bundles on C with bicanonical determinant. In this paper such a matter is reconstructed in modern terms from the modular point of view. In particular, the stratification of the family of scrolls R by Sing R is considered and the cases where R has multiplicity ≥ 3 along a curve are described.