The Geometric Syzygy Conjecture in Even Genus
Michael Kemeny
TL;DR
This paper proves the Geometric Syzygy Conjecture for generic canonical curves of even genus, extending classical results on the generation of their ideals by rank four quadrics to the highest linear syzygy group.
Contribution
It establishes the conjecture for even genus curves, advancing understanding of the syzygy structure of canonical curves.
Findings
Proves the conjecture for generic even genus curves
Extends Green's classical results to the highest linear syzygy group
Enhances knowledge of the algebraic structure of canonical curves
Abstract
We prove the Geometric Syzygy Conjecture for generic canonical curves of even genus. This result extends Green's classical result on the generation of the ideal of a canonical curve by rank four quadrics to the highest linear syzygy group.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation