A stratification of the moduli space of pointed non-singular curves

We consider the moduli space of pointed non-singular curves of genus g whose Weierstrass gap sequence has the largest gap \(\ell _g\) equal to \(2g-3\). We stratify the moduli space by the sequence of osculating divisors associated to a canonically embedded curve. A monomial basis for the space of higher orders regular differentials on the curves in each stratum is constructed. Numerical conditions are given on the semigroup imposing that one of the strata is empty. Several examples are presented.