Curves of degree r+2 in P-r: Cohomological, geometric, and homological aspects

Let C subset of or equal to P-K(r) be a non-degenerate projective curve of degree r + 2, where r greater than or equal to 3. By means of the Hartshorn e-Rao module of C we distinguish 4 different possible cases (and an excepti onal case which only appears if r = 3). In any case C is obtained either by means of an embedding of an arbitrary smooth curve C-0 of genus 2, or by p rojecting an elliptic normal curve from a point or by projecting a rational normal curve from a line. Finally, the possible minimal free resolutions o f the homogeneous coordinate ring of C are studied. (C) 2001 Academic Press .