Curves of Degree r + 2 in r: Cohomological, Geometric, and Homological Aspects,

Let rk be a non-degenerate projective curve of degree r + 2, where r ≥ 3. By means of the Hartshorne–Rao module of we distinguish 4 different possible cases (and an exceptional case which only appears if r = 3). In any case is obtained either by means of an embedding of an arbitrary smooth curve 0 of genus 2, or by projecting an elliptic normal curve from a point or by projecting a rational normal curve from a line. Finally, the possible minimal free resolutions of the homogeneous coordinate ring of are studied.