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The Weierstrass semigroups on the quotient curve of a plane curve of degree \(\leqslant 7\) by an involution. (English) Zbl 1171.14020
Summary: First we describe the Weierstrass semigroups on a plane curve of degree \(\leqslant 6\). Using this description we determine the Weierstrass semigroups at a ramification point and a branch point on a double covering from a plane curve of degree \(\leqslant 6\). In the case of a double covering from a plane curve of degree 7 we determine all the Weierstrass semigroups at branch points.

MSC:
14H51 Special divisors on curves (gonality, Brill-Noether theory)
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