Abstract
In a number of papers by Edge, and in a related paper by Fano, several properties are discussed about the family of scrolls \(R \subset \mathbb {P}^3\) of degree 8 whose plane sections are projected bicanonical models of a genus 3 curve C. This beautiful classical subject is implicitly 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 \(\mathrm{Sing}\,R\) is considered and the cases where R has multiplicity \(\geqslant 3\) along a curve are described.
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Partially supported by PRIN Project Geometry of Algebraic Varieties and by INdAM-GNSAGA.
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Verra, A. Edge and Fano on nets of quadrics. European Journal of Mathematics 4, 1264–1277 (2018). https://doi.org/10.1007/s40879-018-0252-y
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DOI: https://doi.org/10.1007/s40879-018-0252-y