This analysis defines Weierstrass semigroups of ramification points on double covers, explaining their role in hyperelliptic and non-hyperelliptic curves.
The author studies Weierstrass semigroups of ramification points on double covers of curves over ordinary points. It is showed that hyperelliptic curves and non-hyperelliptic curves are characterized by the Weierstrass semigroups.
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Jiryo Komeda (2017) studied this question.
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