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Weierstrass semigroups and the canonical ideal of non-trigonal curves. (English) Zbl 0742.14029
The author studies Weierstraß gap sequences for non-hyperelliptic complete irreducible algebraic curves over an algebraically closed field of arbitrary characteristic. Using the canonical embedding and his result on Weierstraß semigroups he gives (under certain restrictions) an explicit monomial basis for the space of \(n\)-fold regular differentials. He gives a criterion of non-trigonality in terms of the Weierstraß gap sequences and constructs in this case a minimal set of generators of the canonical ideal.

14H55 Riemann surfaces; Weierstrass points; gap sequences
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