Geometry of elliptic normal curves of degree 6

Abstract

In our work we focus on the geometry of elliptic normal curves of degree 6 embedded in . We determine the space of quadric hypersurfaces through an elliptic normal curve of degree 6 and find the explicit equations of generators of . We study the images and of a sextic under the projection from a general point and a general line . In particular, we show that is k-normal for all and is generated by three homogeneous polynomials of degree 2 and two homogeneous polynomials of degree 3. We then show that is k-normal for all and is generated by two homogeneous polynomials of degree 3 and three homogeneous polynomials of degree 4.