TL;DR
This paper revisits the properties of degree 8 scrolls in complex projective space related to genus 3 curves, using modern modular methods to connect geometric features with vector bundle moduli.
Contribution
It provides a modern modular reinterpretation of classical results on degree 8 scrolls and their relation to vector bundle moduli on genus 3 curves.
Findings
Reconstruction of classical properties of degree 8 scrolls using modern methods
Connection established between scrolls and moduli of semistable vector bundles
Enhanced understanding of the geometric and algebraic structure of the family of scrolls
Abstract
In a number of papers by Edge, and in a related paper by Fano, several properties are discussed of the family of scrolls of degree 8, in the complex projective space, whose plane sections are projected bicanonical models of a genus 3 curve C. This beautiful subject is implicitely related to the moduli of semistable rank two vector bundles on C with bicanonical determinant. We revisit and reconstruct this matter in modern terms with a modular point of view. This paper is the refereed version of a contribution to a volume in honor of W.L Edge, to be published by European Journal of Mathematics.
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