The ideal of curves of genus 2 on rational normal scrolls

2011/02/15 by Hofmann, Andrea
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1102.3156

Abstract

Given a smooth curve of genus 2 embedded in P^(d-2) with a complete linear system of degree d>=6, we list all types of rational normal scrolls arising from linear systems g¹₂ and g¹₃ on C. Furthermore, we give a description of the ideal of such a curve of genus 2 embedded in P^(d-2) as a sum of the ideal of the two-dimensional scroll defined by the unique g¹₂ on C and the ideal of a three-dimensional scroll arising from a g¹₃ on C and not containing the scroll defined by the g¹₂ on C.

Related

• Scrolls containing binary curves
• Projective normality of special scrolls
• The generic special scroll of genus g in Pn. Special scrolls in P3
• The degree of the third secant variety of a smooth curve of genus 2
• Curves with Canonical Models on Scrolls