The ideal of curves of genus 2 on rational normal scrolls

Details The ideal of curves of genus 2 on rational normal scrolls The ideal of curves of genus 2 on rational normal scrolls

2011-02-15

arxiv.org/abs/1102.3156v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

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 g^1_2 and g^1_3 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 g^1_2 on C and the ideal of a three-dimensional scroll arising from a g^1_3 on C and not containing the scroll defined by the g^1_2 on C.

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