SUBCANONICAL POINTS ON ALGEBRAIC CURVES

If C is a smooth, complete algebraic curve of genus g >= 2 over the complex numbers, a point p of C is subcanonical if K-C congruent to O-C ((2g - 2)p). We study the locus G(g) subset of M-g,M-1 of pointed curves (C, p), where p is a subcanonical point of C. Subcanonical points are Weierstrass points, and we study their associated Weierstrass gap sequences. In particular, we find the Weierstrass gap sequence at a general point of each component of G(g) and construct subcanonical points with other gap sequences as ramification points of certain cyclic covers and describe all possible gap sequences for g <= 6.