Abstract
If C C is a smooth, complete algebraic curve of genus g ≥ 2 g\geq 2 over the complex numbers, a point p p of C C is subcanonical if K C ≅ O C ( ( 2 g − 2 ) p ) K_C \cong \mathcal {O}_C\big ((2g-2)p\big ) . We study the locus G g ⊆ M g , 1 \mathcal {G}_g\subseteq \mathcal {M}_{g,1} of pointed curves ( C , p ) (C,p) , where p p is a subcanonical point of C 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 \mathcal {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 g\leq 6 .
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