Extensions and paracanonical curves of genus 6

2024/02/14 by Schreyer, Frank-Olaf, Truong, Hoang Le
#14C05 (primary) #14D07 #14D20 #14E08 (secondary) #14J26 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.09351

Abstract

In this note we give a computationally easy to use method to compute a maximal extension of certain varieties. As a application we prove that a general paracanonical curve C genus 6 as a codimension three subvarieties of P⁴ extend to precisely 26 families of surfaces Y in P⁵.

Related

• The genus of curves in \mathbb P⁴ and \mathbb P⁵ not contained in quadrics
• Extensions of curves with high degree with respect to the genus
• A census of genus 6 curves over \mathbbF₂
• Counting curves of any genus on P²₆
• Genus six curves, K3 surfaces, and stable pairs