Green's conjecture for binary curves
Marco Franciosi, Elisa Tenni
TL;DR
This paper proves that Green's conjecture, which relates to the syzygies of canonical curves, holds for generic binary curves by analyzing the scrolls containing rational normal curves.
Contribution
It establishes the validity of Green's conjecture for a new class of curves, specifically generic binary curves, using a detailed geometric analysis.
Findings
Green's conjecture holds for generic binary curves
Analysis of scrolls containing rational normal curves
Supports conjecture's validity in broader contexts
Abstract
We show that Generic Green's conjecture holds for generic binary curves, through a detailed analysis of the family of scrolls containing fixed rational normal curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation